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Auf dieser Seite finden Sie Informationen über Vorträge folgender Seminare:

  • Rhein-Main Kolloquium Stochastik (Gemeinsames Kolloquium der Arbeitsgruppen Stochastik TU Darmstadt / Gutenberg-Universität Mainz / Goethe-Universität Frankfurt)
  • Stochastisches Kolloquium (Forschungsseminar des Schwerpunkts Stochastik)
  • Oberseminar Stochastik (Forschungsseminar für Doktoranden und Masterstudenten)
  • Verweis auf weitere interessante Vorträge (außerhalb des Frankfurter Schwerpunkts Stochastik)

 

Vorträge in chronologischer Reihenfolge


Rhein-Main-Kolloquium Stochastik

Freitag, 02.02.2024, Raum 711 groß, Robert-Mayer-Straße 10

Alessandra Bianchi, Università degli Studi di Padova

 

Random walks on a Lévy-type random media 

 

We consider a one-dimensional process in random media that generalizes the model known in the physical literature as Lévy-Lorentz gas. The medium is provided by a renewal point process in which the inter-distances between points are i.i.d. heavy-tailed random variables, while the dynamics is obtained as the linear interpolation of - possibly long jump - random walks on the point process. These models have been used to describe phenomena that exhibit superdiffusion, and the main focus of this investigation is on the derivation of the scaling behavior of the process as a function of the parameters that enter its definition.

We give an account on a number of recent theorems, which include non-standard functional limit theorems for the process in discrete and continuous time, and the distributional characterization of the first-passage time. We conclude by discussing the two-dimensional setting and some related open problems.

 

Peter Mörters, University of Cologne

 

Condensation in scale-free geometric graphs with excess edges

 

We identify the upper large deviation probability for the number of edges in scale-free geometric random graph models as the space volume goes to infinity. Our result covers the models of scale-free percolation, the Boolean model with heavy-tailed radius distribution, and the age-dependent random connection model. In all these cases the mechanism behind the large deviation is based on a condensation effect for the vertex degrees. The mechanism randomly selects a finite number of vertices and increases their power, so that they connect to a macroscopic number of vertices in the graph, while the other vertices retain a degree close to their expectation and thus make no more than the expected contribution to the large deviation event. We also study the empirical distribution of edge lengths under the conditioning, which splits into a bulk and travelling wave part of asymptotically positive proportions. The talk is based on joint work with Remco van der Hofstad, Pim van der Hoorn, Céline Kerriou and Neeladri Maitra.


Frankfurter Seminar

Mittwoch, 24.01.2024, Raum 711 groß und klein, Robert-Mayer-Straße 10

- ausgefallen - 


Frankfurter Seminar

Mittwoch, 22.11.2023, Raum 711 groß und klein, Robert-Mayer-Straße 10


Frankfurter Seminar

Mittwoch, 08.11.2023, Raum 711 groß und klein, Robert-Mayer-Straße 10


Oberseminar Stochastik

Mittwoch, 18.10.2023, in Präsenz, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Masterarbeit von Annika Meyer (Goethe Universität Frankfurt)

Title: tba

Rhein-Main-Kolloquium Stochastik

Freitag, 07.07.2023, Raum 711 groß, Robert-Mayer Straße 10

Sprecher: Prof. David Prömel (Uni Mannheim), 15:15 Uhr

Titel: Model-free portfolio theory: a rough path approach

Abstract: Classical approaches to optimal portfolio selection problems are based on probabilistic models for the asset returns or prices. However, by now it is well observed that the performance of optimal portfolios are highly sensitive to model misspecifications. To account for various type of model risk, robust and model-free approaches have gained more and more importance in portfolio theory. Using rough path theory, we provide a pathwise foundation for stochastic Ito integration, which covers most commonly applied trading strategies and mathematical models of financial markets possibly under model uncertainty. Based on this pathwise foundation, we develop a model-free approach to stochastic portfolio theory and Cover's universal portfolio. The use of rough path theory allows for treating significantly more general portfolios in a model-free setting, compared to previous model-free approaches.
The talk is based on joint works with Andrew Allan, Christa Cuchiero and Chong Liu.

Sprecher: Prof. Christoph Czichowsky (LSE), 16:45 Uhr

Titel: Hedging and portfolio optimisation in rough volatility models 

Abstract: Rough volatility models have become quite popular recently, as they capture both the fractional scaling of the time series of the historic volatility (Gatheral et al. 2018) and the behaviour of the implied volatility surface (Fukasawa 2011, Bayer et al. 2016) remarkably well. In contrast to classical stochastic volatility models, the volatility process is neither a Markov process nor a semimartingale. Therefore, these models fall outside the scope of standard stochastic analysis and provide new mathematical challenges. In this talk, we present an overview of of this new paradigm in volatility modelling and consider the impact of rough volatility on hedging and portfolio optimisation.The talk is based on joint works with David Martins, Johannes Muhle-Karbe and Denis Schelling.


Frankfurter Seminar

Mittwoch, 28.06.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Michael Joswig (TU Berlin)

Titel: tba


Frankfurter Seminar

Mittwoch, 07.06.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Carla Cederbaum (Universität Tübingen)

Titel: tba


Stochastisches Kolloquium

Mittwoch, 31.05.2023, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Prof. Wolfgang Woess (TU Graz)

Title: Boundary behaviour of branching Markov chains

Abstract: We study multi-type branching Markov chains on denumerable type spaces in discrete time. The way of thinking is in the sense that the type space carries a structure, e.g., of a graph with certain geometric properties to be specified, and that the population moves at random in space, so that the types are considered as sites. It is supposed that the offspring distributions satisfy a uniform "L log L" moment condition with type-independent expected offspring number, and that the associated "base" Markov chain on the space is transient and irreducible. Given the population at time n at the different sites, we normalize it by dividing by its total number. The resulting empirical distribution is a random probability measure on the type space. Assuming that the latter is equipped with  a "geometric" compactification with a boundary at infinity, a main focus is on the question whether the sequence of empirical distributions converges a.s. weakly to a random probability distribution on the boundary.

This is joint work with Vadim A. Kaimanovich (Ottawa), to appear in Ann. Inst. H. Poincaré Prob. Stat.


Frankfurter Seminar

Mittwoch, 10.05.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Renzo Cavalieri (Colorado State University, Fort Collins)

Titel: tba


Frankfurter Seminar

Mittwoch, 19.04.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Jean-François Le Gall (Université Paris-Saclay)

Titel: Recent developments in random geometry


Oberseminar Stochastik

Mittwoch, 12.04.2023, in Präsenz, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Fabian Roth (Goethe Universität Frankfurt)

Title: AlphaZero, Stochastic MuZero & Co: Strengths and limitations of state-of-the-art reinforcement learning algorithms that involve planning

Stochastisches Kolloquium

Mittwoch, 15.02.2023, Beginn 14.00 h, in Raum 711 groß.

14:00 Uhr: Dr. Charline Smadi (INRAE und Institut Fourier, Université Grenoble)

Titel: Quasi-equilibria and click times for a variant of Muller's ratchet

Abstract: We will introduce and study a variant of a well-known model in population genetics, named Muller's ratchet, which is seen as one explanation of the ubiquity of sexual selection in Nature. Consider a population of N individuals, each of them carrying a type in \N_0. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type k has the same selective advantage over all individuals with type k′>k, and type k mutates to type k+1 at a constant rate (in the classical Muller's ratchet, the selective advantage is proportional to k′−k). For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the click times of the ratchet (i.e. the times at which the hitherto minimal (`best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a ``dual'' hierarchical multitype logistic system. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations. 

This is a joint work with A. González Casanova and Anton Wakolbinger.


Stochastisches Kolloquium

Mittwoch, 25. Januar 2023, Raum 711 groß

14:15 Uhr: Prof. Dr. Noela Müller (TU Eindhoven)

Title: The rank of sparse symmetric matrices over arbitrary fields

Abstract: Let F be an arbitrary field and (G_{n,d/n})_n be a sequence of sparse weighted Erdős-Rényi random graphs on n vertices with edge probability d/n, whose edge weights are drawn from F \{0} according to a matrix J_n. We show that the normalised rank of the adjacency matrix of (G_{n,d/n})_n converges in probability to a constant, and derive the limiting expression. Our result shows that for the general class of sparse symmetric matrices under consideration, the asymptotics of the normalised rank are independent of the edge weights and even the field, in the sense that the limiting constant for the general case coincides with the one previously established for adjacency matrices of sparse (non-weighted) Erdős-Rényi matrices over R in the seminal work of Bordenave, Lelarge and Salez. Our proof, which is purely combinatorial in its nature, is based on an intricate adaptation of the novel perturbation method of Coja-Oghlan, Ergür, Gao, Hetterich and Rolvien to the symmetric setting.

This is joint work with Rem co van der Hofstad and Haodong Zhu.


Oberseminar Stochastik

Mittwoch, 18. Januar 2023, in Präsenz, Raum 711 groß 

14:15 Uhr: Simon Arendt (Goethe Universität Frankfurt)

Title: Austauschbare Arrays

Abstract: Der funktionale Darstellungssatz von Aldous-Hoover-Kallenberg verallgemeinert den Satz von de Finetti auf mehrdimensionale austauschbare Arrays. Im Vortrag wird der Spezialfall zwei-dimensionaler Arrays vorgestellt. Neben dem formalen Beweis diskutieren wir als praktische Anwendung die Implikationen des Darstellungssatzes für die Bayes-Statistik mit relationalen Daten.


Rhein-Main-Kolloquium Stochastik (in Präsenz)

Am Freitag, 13.01.2023, Raum 711 groß, Robert-Mayer Straße 10

Krankheitsbedingt entfällt leider der erste Vortrag von Herrn Dr. Hermann.
Der Beginn verändert sich auf 16.00 Uhr !

16.00 Uhr "Kaffeepause"

16.45 Uhr  Beginn des Vortrages von Herrn Dr. Marcel Ortgiese, (University of Bath)

Sprecher: Dr. Marcel Ortgiese (University of Bath)

Titel: “The contact process on tree-like graphs"

Abstract: The contact process is a simple model for the spread of an infection in a structured population. I will first survey some of the recent results for the contact process when the underlying graph is either a finite or infinite random graph that is locally tree-like. The main focus of the talk will be to understand what changes when the underlying graph also evolves over time. We will look both at the case when edges update independently of the infection, but also the dependent case. In the latter case, the random graph reacts to the infection by only resampling connections to neighbours that are infected. The main question we will answer is first of all whether the contact process exhibits a phase transition. If it does, we will look at how the phase transition depends on the underlying graph dynamics.


Oberseminar Stochastik

Mittwoch, 7. Dezember 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Tessa Feller (Goethe Universität Frankfurt)

Title: Neues zum Lemma von Johnson-Lindenstrauss


Oberseminar Stochastik

Mittwoch, 2. November 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Marie Kuhn (Goethe Universität Frankfurt)

Title: Modeling neuronal spike trains with Hawkes processes


Oberseminar Stochastik

Mittwoch, 19. Oktober 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Jasper Ischebeck (Goethe Universität Frankfurt)

Rhein-Main-Kolloquium Stochastik (in Präsenz)

Freitag, 01.07.2022, Raum 711 groß, Robert-Mayer Straße 10

Dr. Julian Gerstenberg (Goethe Universität Frankfurt), 15:15 Uhr
Dr. Jonathan Warren (University of Warwick), 16:45 Uhr

Sprecher: Dr. Julian Gerstenberg
Titel: Functional Representation Theorems for Exchangeable Laws
Abstract: Functional Representation theorems (FRTs) for exchangeable random objects exist for many types of data structures, for example sequences (de Finetti/Hewitt-Savage), partitions (Kingman), hierarchical structures, graphs or more general array-like data structures (Aldous-Hoover-Kallenberg).  In this talk several known FRTs are presented and the language of category theory [vocabulary: cagegory, functor, natural transformation] is used to introduce an abstract concept of data structures, which allows for a unified formulation of many known FRTs. This leads to a conjecture about a "General FRT".  No knowledge of category theory is assumed to follow this talk, the concepts will be motivated by statistical practise. This research is funded by the DFG project 502386356. 

Sprecher: Dr. Jonathan Warren, Universty of Warwick
Titel: At the edge of a cloud of Brownian particles
Abstract: The talk concerns a model for the motion of particles carried in a turbulent fluid in which a single particle moves according to an SDE of the form dX_t= \sigma dB_t + dW(t,X_t). Here, W is a Gaussian field, describing the environment, and B is an independent Brownian motion representing some additional diffusivity. We are interested in the behaviour at large times, but far from the origin.  There,  we find a transition which is analogous to that between weak and strong disorder for polymer models, and at the transition the stochastic heat equation appears.



Oberseminar Stochastik:

Am Mittwoch, 29.06.2022, in Präsenz, Raum 711 groß, 14:15 Uhr

Philipp Klein (Magdeburg) 

Anomaly detection based on MOSUM statistics in large image data

Abstract:

Being able to identify anomalies in image data is important in many practical applications. This includes the detection of cancerous cells in medicine, obstacles in autonomous driving and fissures in the construction material of buildings. When the data is large, it is oftentimes helpful to have an efficient pre-processing procedure to identify areas potentially containing anomalies. This holds especially true when these anomalies are sparse.
We develop a procedure for the detection of fissures in 2D image data based on moving sum (MOSUM) statistics. In particular, based on the observation of local geometric properties of fissures and natural anomalies in concrete, we use a combination of moving semicircle- and 'rectangle'-shaped windows in order to identify regions that potentially have fissures. Under the null assumption of no anomalies for P-dimensional image data, we are able to show convergence for MOSUM statistics using a general class of scan windows fulfilling (weak) regularity conditions towards functionals of P-parameter Gaussian processes. In particular, this class includes 2D convex sets that we use for fissure detection.


Die Identifikation von Anomalien in Bilddaten ist in vielen praktischen Anwendungen von großer Bedeutung. Dazu zählen die Erkennung von Krebszellen, das Wahrnehmen von Hindernissen beim autonomen Fahren sowie die Detektion von Rissen in Baumaterial. Bei großen Datenmengen ist es oftmals hilfreich, ein effizientes Vorverarbeitungsverfahren zu haben, welches dabei hilft, mögliche Regionen mit Anomalien zu identifizieren. Dies trifft besonders dann zu, wenn die Anomalien nur einen sehr kleinen Teil des Datensatzes ausmachen. Mithilfe  so genannter 'moving sum' (MOSUM)-Statistiken entwickeln wir ein Verfahren zur Erkennung von Rissen in zweidimensionalen Daten. Basierend auf lokalen geometrischen Eigenschaften von Rissen und natürlichen Anomalien verwenden wir kreisförmige und 'rechteckige' Fenster zur Identifikation von Regionen, die möglicherweise Risse enthalten. Unter der Nullannahme der Nichtexistenz von Anomalien in P-dimensionalen Bilddaten zeigen wir schwache Konvergenz für MOSUM-Statistiken, die eine allgemeine Klassen von Scan-Fenstern verwendet, gegen Funktionale von P-Parameter Gaußprozessen. Diese Klasse beinhaltet insbesondere zweidimensionale konvexe Mengen, welche wir für die Risserkennung verwenden.


Am Mittwoch, 08.06.2022, in Präsenz, Raum 711 groß,

15:15 Uhr
Terence Tsui Ho Lung (Oxford)
Uncovering genealogy of superprocesses through lookdown constructions

Abstract: In this talk, I will demonstrate how one can uncover genealogical structures and ancestral lineages of spatially-structured population through the means of lookdown constructions. By enriching a spatially-structured population with levels imposed on individual particles that follows carefully selected dynamics, one can introduce a spatial-level Markovian population that enables us to trace the motion of ancestral lineages of the underlying spatial population. In particular, we study populations with a juvenile and adult stage, and show their many possible scaling limits with rich dynamics. Finally, we explain how we use a lookdown construction to derive the motion of ancestral lineages in these scaling limits.

16:30 Uhr
Adrian Martini (Oxford)
Modelling Aggregation and Dormancy in the Life Cycle of Dictyostelium discoideum

Abstract: The amoeba Dictyostelium discoideum transitions from unicellular to multicellular life when food is scarce. To avoid extinction, individuals aggregate, form complex fruiting bodies and disperse spores for new amoebae to hatch under favourable conditions. Additionally, spores may delay their hatching process in a phenomenon called dormancy. The population uses dormancy to reduce risk in the presence of environmental fluctuations.
We seek to understand the dynamics that lead to the formation of fruiting bodies and aim to quantify the spread of advantageous alleles under dormancy. In the first part of the talk, we replicate the formation of aggregates under the influence of noise by introducing an approximate Stochastic PDE. In the second part, we review recent results on dormancy and discuss possible extensions.

Berufspraxiskolloquium:

Am 23.6.22. (Do) um 18 c.t., Raum 711 groß, findet das nächste Berufspraxiskolloquium statt, zu dem alle Interessierten herzlich eingeladen sind. 

Vortragender: Dr. Patrick Liebrich (Emcore) 

Titel: Der Finanzplatz Liechtenstein

Zusammenfassung:

Das Fürstentum Liechtenstein bietet durch seine Lage in der Schweizer Zollunion und dem EWR hervorragende steuerliche und rechtliche Rahmenbedingungen. So ist der Kleinstaat Sitz vieler europäisch agierender Finanzdienstleister. Und doch unterscheidet sich die Art der hier ansässigen Unternehmen deutlich von denen in den grossen Finanzzentren wie Frankfurt. In dem Vortrag wird der Finanzplatz Liechtenstein mit seinen Besonderheiten vorgestellt.

Oberseminar Stochastik:

Mittwoch, 04. Mai 2022, in Präsenz, Raum 711 groß

14:15 Uhr:Masterarbeit von Marina Sturm:

Nichtparametrische Statistik zur Detektion von Richtungswechseln in Organellenbewegungen

Oberseminar Stochastik:

Mittwoch, 09. Februar 2022, via Zoom

14:15 Uhr: Solveig Plomer zum aktuellen Stand ihres Promotionsprojekts:

Detecting changes in movement direction and speed in cell organelles
 


Oberseminar Stochastik:

Mittwoch, 15. Dezember 2021, via Zoom

https://uni-frankfurt.zoom.us/j/97187235503?pwd=Njg5bTUxZlhQdmNJMHd0MUtxOFVHdz09

14:15 Uhr:  Masterarbeit von Herrn Robin Masic:

Methoden der Richtungsstatistik mit Anwendung auf Plastid-Bewegungen
 
 

 

Berufspraxiskolloquium:

Das Kolloquium richtet sich speziell an Studierende und soll Einblicke in spätere Berufsfelder geben. Es ist eine Kombination aus einer Firmenvorstellung und einem Vortrag über die Anwendung mathematischer Methoden in der Berufspraxis.

Am 9.12. (Do) um 18:15 (!) findet das nächste Berufspraxiskolloquium per Zoom statt, zu dem alle Interessierten herzlich eingeladen sind.

Referenten: Christian Braun und Nadine Mbenda (PricewaterhouseCoopers | Risk & Regulation)

Titel: Quantitatives Kreditrisikomanagement: Einführung und aktuelle Herausforderungen

Zusammenfassung: Das Credit Risk Quant-Team von PwC Deutschland wird die Dimensionen des Kreditrisikos, wesentliche Risikomodelle, die Ermittlung der Risikovorsorge unter IFRS 9 und die aktuellen Herausforderungen bei der Kreditrisikomodellierung vorstellen.

Herr Prof. Dr. Christoph Kühn lädt Sie zu diesem Zoom-Meeting ein.

Thema: Berufspraxiskolloquium
Uhrzeit: 9.Dez..2021 06:00 PM Amsterdam, Berlin, Rom, Stockholm, Wien

Zoom-Meeting beitreten
https://uni-frankfurt.zoom.us/j/95253176690?pwd=RmVoZ1RRWEhhU3hGQ3hocGdVT3VXUT09

Meeting-ID: 952 5317 6690
Kenncode: 772102


Rhein-Main-Kolloquium Stochastik:

 

 

Freitag, 03.12.2021 - via Zoom.

https://uni-frankfurt.zoom.us/j/93449699353?pwd=Wm5GNE90Qk90K0o0cjIxb3AvanFIUT09

Meeting ID: 934 4969 9353
Passcode: 828632

15:15-16:15: Nina Gantert (TU München)

16:15-16:45: (virtual) coffee break

16:45-17:45: Paolo Dai Pra (Università degli Studi di Verona)

Nina Gantert (TU München)

Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation

Abstract: We study the asymptotics of the k-regular self-similar fragmentation process. For α>0 and an integer k≥2, this is the Markov process (I_t)_{t≥0} in which each It is a union of open subsets of [0,1), and independently each subinterval of It of size u breaks into k equally sized pieces at rate u^α. Let k^{−mt} and k^{−Mt} be the respective sizes of the largest and smallest fragments in I_t. By relating (I_t)_{t≥0} to a branching random walk, we find that there exist explicit deterministic functions g(t) and h(t) such that |mt−g(t)|≤1 and |Mt−h(t)|≤1 for all sufficiently large t. Furthermore, for each n, we study the final time at which fragments of size k^{-n} exist. In particular, by relating our branching random walk to a certain point process, we show that, after suitable rescaling, the laws of these times converge to a Gumbel distribution as n→∞.

Based on joint work with Piotr Dyszewski, Samuel G. G. Johnston, Joscha Prochno and Dominik Schmid

Paolo Dai Pra (Università degli Studi di Verona)

Self-sustained oscillations in interacting systems: an overview and some recent advances

Abstract: Self organized collective periodic behavior is seen to emerge in several different contexts: from neuroscience to tectonic plates movements, from population dynamics to epidemiology. A large variety of stochastic models have been proposed to capture this phenomenon at a mathematical level, showing that it may be induced by a combination of factors including noise, dissipation, loss of Markovianity and/or of time reversibility. Most of the present literature concerns mean-field models, where the thermodynamic limit is well understood at a dynamical level, and the emergence of oscillations can be seen from the macroscopic evolution equations. In models with short range interaction it is much harder to understand how self organization at microscopic level may produce large scale rhythms. Some partial results have been obtained for a non-reversible modification of the nearest neighbour Ising model.


 

Berufspraxiskolloquium:

Das Kolloquium richtet sich speziell an Studierende und soll Einblicke in spätere Berufsfelder geben. Es ist eine Kombination aus einer Firmenvorstellung und einem Vortrag über die Anwendung mathematischer Methoden in der Berufspraxis.

Donnerstag den 28.10.2021 um 16:15 via Zoom

Dr. Klaus Rinne (Ernst & Young, FAAS Quant Team)

Titel: Valuation of interest rate options under negative rates
Table of Content: - Introduction to the concept of volatility - Interest rate cap & floor - Working as a quant at EY

Zoom-Meeting beitreten
https://uni-frankfurt.zoom.us/j/95253176690?pwd=RmVoZ1RRWEhhU3hGQ3hocGdVT3VXUT09

Meeting-ID: 952 5317 6690
Kenncode: 772102

Oberseminar Stochastik:

Dienstag, 27. Juli 2021, via ZOOM

https://uni-frankfurt.zoom.us/j/96877275138?pwd=azBCSGNKZTd4elBnT0lKNjhlWHVMUT09

Meeting-ID: 968 7727 5138
Kenncode: 322615

10:00 Uhr: Master-Abschlussvortrag von Niyat Isayas

Rekonstruktionsprobleme an rein zufälligen rekursiven Bäumen


 

Oberseminar Stochastik:

Mittwoch, 30. Juni 2021, via ZOOM

Zugangsdaten bitte über Apl. Prof. Dr. Gaby Schneider anfragen.

14:15 Uhr: Master-Abschlussvortrag Fabian Schneider

Ein multivariater Ansatz zur Analyse der Fütteraktivität von Bienen


MathFinanceColloquium/ Berufspraxiskolloquium:

Dienstag, 29.06.2021, 14:15 Uhr via ZOOM

Zugangsdaten bitte über Prof. Dr. Christoph Kühn anfragen.

Referenten:
Kasra Khani (Consultant, d-fine)
Dr. Hans-Peter Wächter (Partner, d-fine)

Titel:
The Endgame of Libor – Einstieg als Finanzmathematiker in einer Zeit voller Veränderungen

Beschreibung:
d-fine ist mit mehr als 1000 Mitarbeiterinnen und Mitarbeitern eines der führenden Beratungsunternehmen für quantitativ und technologisch anspruchsvolle Projekte. Nach einer Vorstellung der Firma möchten wir Ihnen gerne die Benchmark Reform im Rahmen von USA Studentenkrediten vorstellen. Unser Vortrag thematisiert hierbei insbesondere den Projektalltag und die besonderen Erfahrungen als Einsteiger in Zeiten der Pandemie.

Alle (theoretisch oder praktisch) Interessierten sind herzlich eingeladen!


Rhein-Main-Kolloquium Stochastik:

Freitag, 11.06.2021: ONLINE-Veranstaltung

Zoom access to the talks:

https://uni-frankfurt.zoom.us/j/94648348387?pwd=anVJNnJKY2NZTVBGZWR4UXdGRHpOUT09

Meeting ID: 946 4834 8387

Passcode: 969450

15:15-16:15: Gaultier Lambert (Zürich)

16:15-16:45: virtual coffee break

16:45-17:45: Christian Brennecke (Harvard)

Gaultier Lambert

Title: Normal approximation for traces of random unitary matrices

This talk aim to report on the fluctuations of traces of powers of a random n by n matrix U distributed according to the Haar measure on the unitary group. This classical random matrix problem has been extensively studied using several different methods such as asymptotics of Toeplitz determinants, representation theory, loop equations etc. It turns out that for any k≥1, Tr[U^k] converges as n tends to infinity to a Gaussian random variable with a super exponential rate of convergence. In this talk, I will explain some of these results and present some recent work with Kurt Johansson (KTH) in which we revisited this problem in a multivariate setting.

Christian Brennecke

Title: On the TAP equations for the Sherrington-Kirkpatrick Model

In this talk, I will review the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass and present a dynamical derivation, valid at sufficiently high temperature. In our derivation, the TAP equations follow as a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish decay of higher order correlation functions. We illustrate this by proving a suitable decay bound on the three point functions which implies an analogue of the TAP equations for the two point functions. The talk is based on joint work with A. Adhikari, P. von Soosten and H.T. Yau.


Stochastisches Kolloquium:

Freitag, 28. Mai 2021 via ZOOM

https://uni-frankfurt.zoom.us/j/95773112662?pwd=NVZFSG1tdytoQlpFSEtHUkxqTzBsQT09

Meeting-ID: 957 7311 2662

Kenncode: 548086

15:15 Uhr: Vortrag von Dr. Jon Warren Department of Statistics, University of Warwick

A family of local times studied as a Markov process

Abstract

 

Oberseminar Stochastik:

Mittwoch, 05. Mai 2021, via ZOOM

https://uni-frankfurt.zoom.us/j/94756581976?pwd=ejZFQjdhRG5GaEdMaDdvM3p3aUY3UT09

Meeting ID: 947 5658 1976
Passcode: 223308

14:30 Uhr: Master-Abschlussvortrag Insea Schlattmeier

Überleben und Wachstum von Parasitenpopulationen in räumlich strukturierten Wirtspopulationen

Oberseminar Stochastik:

Mittwoch, 24. März 2021, via ZOOM

Zugangsdaten bitte über Prof. Dr. Wakolbinger anfragen

14:30 Uhr: Master-Abschlussvortrag Jan Lukas Igelbrink

Langreichweitige Seedbank-Koaleszenten und fraktionale Brownbewegungen


 

Rhein-Main-Kolloquium Stochastik:

Freitag, 29.01.2021: ONLINE-Veranstaltung

Zoom access to the talks:
https://uni-frankfurt.zoom.us/j/91292915620?pwd=QkR5THI0MklWWDR1ajBoUytFOXBwUT09

Meeting-ID: 912 9291 5620
Code: 109618

15:15-16:15: Gabor Lugosi (Pompeu Fabra University, Barcelona)

16:15-16:45: virtual coffee break

16:45-17:45: Po-Ling Loh (University of Cambridge)

Gábor Lugosi

Title: Root finding and broadcasting in random recursive trees

Abstract: Uniform and preferential attachment trees are among the simplest examples of dynamically growing networks. The statistical problems we address in this talk regard discovering the past of the tree when a present-day snapshot is observed. We present a few results that show that, even in gigantic networks, a lot of information is preserved from the very early days. In particular, we discuss the problem of finding the root and the broadcasting problem.


Po-Ling Loh

Title: Statistical inference for infectious disease modeling

Abstract: We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. Furthermore, we prove that the confidence sets are almost surely persistent, i.e., they settle down after a finite number of time steps. In the second scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test.

This is joint work with Justin Khim and Varun Jog.


Oberseminar Stochastik:

Mittwoch, 16. Dezember 2020, VidyoConnect

Zugangsdaten bitte über Prof. Dr. Neininger anfragen

14:15 Uhr: Master-Abschlussvortrag Ân Hòang

Zur Struktur zufälliger Permutationen, GEM- und Poisson-Dirichlet-Verteilungen


Oberseminar Stochastik:

Mittwoch, 14. Oktober 2020

14:15 Uhr: Master-Abschlussvortrag Denis Spiegel

Convergence Rates in Distributional Reinforcement Learning

Rhein-Main-Kolloquium Stochastik:

Freitag, 29.05.2020: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Giada Basile (Universität Rom): Titel tba

16.15-16.45 Uhr Kaffeepause

16.15 Uhr (tba)

Stochastisches Kolloquium:

Mittwoch, 22. Januar 2020, 14:15 Uhr in Raum 711 gr

14:00 Uhr: Vortrag von Dr. Charline Smadi, Universität Grenoble

Crossing a fitness valley as a metastable transition in a stochastic population model
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition, and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is an  exponentially distributed random variable.

This is a joint work with Anton Bovier and Loren Coquille


Stochastisches Kolloquium:

Mittwoch, 18. Dezember 2019, 14:15 Uhr in Raum 711 gr

14:00 Uhr: Vortrag von Maurice Georgi

Stochastische Modellierung von segmentweisen linearen Plastidbewegungen


Rhein-Main-Kolloquium Stochastik:

Freitag, 06.12.2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Simone Warzel (TU München): Quantum spin glasses: a mathematical challenge

The theory of classical mean-field spin glasses is a well-established and celebrated field within probability theory. The addition of a constant perpendicular magnetic field introduces a non-commuting term into the energy of such spin glasses and hence causes quantum effects. The main aim of this talk is to give an overview over some of the motivations for the study of quantum spin glasses. I will also review some first mathematical results in this field. Among them is a derivation of the key features of the thermal phase diagram of the simplest of all mean-field spin glasses, the quantum random energy model.

16.15-16.45 Uhr Kaffeepause

16.15 Uhr Matthias Erbar (Bonn): A variational characterization of the Sine_ß point process

The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_ß process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine_ß process. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional. Joint work with Martin Huesmann and Thomas Leblé 

 

MathFinanceColloquium/ Berufspraxiskolloquium:

Donnerstag, 05.12.2019, 16:15 Uhr, Raum 711 groß

Dr. Jürgen Bierbaum (Alte Leipziger Versicherung): Bewertung in unvollständigen Märkten - Finanzmathematik in der Lebensversicherung

Die Mehrzahl der Lebensversicherungsverträge in Deutschland enthält langfristige Zinsgarantien. Die Preisfindung sowie die ökonomische und bilanzielle Bewertung dieser Verträge erfordert die Entwicklung komplexer finanz- und versicherungsmathematischer Modelle. Wegen der Illiquidität der Märkte für langfristige Kapitalanlagen ist auch die Kalibrierung der Bewertungsmodelle eine nichttriviale Aufgabe. Zusätzlich sollte bereits beim Produktdesign auf eine kapitaleffiziente Struktur der Verpflichtungen geachtet werden. Im Vortrag werden einige wichtige Aufgabenstellungen aus der Praxis sowie gängige Ansätze zu ihrer Lösung vorgestellt.

Im Anschluss ist eine kurze Nachsitzung im Frankfurt and Friends geplant.


Gastvortrag:

Montag, 18. November um 12:30 Uhr in Raum 110

Sprecher: Prof. Dr. Dirk Metzler, FB Biologie, LMU München

Hybridzone zwischen Rabenkrähen und Nebelkrähen: Artbildung allein durch Paarungspräferenzen?

Aaskrähen gibt es in zwei Farbmorphen: in Westeuropa als schwarze Rabenkrähen und in Nord-, Ost-, und Südeuropa als grau-schwarz-gemusterte Nebelkrähen. Wo die Verbreitungsgebiete der beiden Farbmorphen an einader grenzen,z.B. in Deutschland an der Elbe, kommt es zur Hybridisierung. Die Krähen scheinen jedoch Verpaarung innerhalb ihrer jeweiligen Farbmorphe zu bevorzugen. Mittels mathematischer Modellierung und numerischen Simulationen untersuchen wir, ob solche assortativen Paarungspräferenzen eine stabile Koexistenz der beiden Farbmorphen erklären kann und eventuell zur Aufspaltung der Aaskrähen in zwei Arten führen wird. Wir passen unser Modell an populationsgenetische Daten an und berücksichtigen die genetische Architektur der Gefiederfärbung. Eine überraschende Vorhersage unserer Modellierung ist, dass die Hybridzone einer räumlichen Dynamik unterliegt, die stark davon abhängt, wie zwei Genloci für die Ausprägung der Gefiederfärbung interagieren. (Kooperation mit Jochen Wolf, Joshua Penalba und Ulrich Knief)
 

Stochastisches Kolloquium:

Mittwoch, 13. November 2019, Raum 711 gr

14:00 Uhr: Vortrag von Prof. Dr. John T Whelan (School of Mathematical Sciences (Statistics), Rochester Institute of Technology and Institute for Theoretical Physics)

Bayesian Applications of the Bradley-Terry Model to Sports Team Ratings

The Bradley-Terry-Zermelo model has been widely used to evaluate paired comparison experiments, with applications ranging from taste tests to rating chess players. In this model, each object being compared has a strength parameter, and the probability of winning a comparison is proportional to this strength. I consider the application of this model to the problem of rating or ranking teams based on their game results when the schedule is not balanced. While the traditional maximum-likelihood implementation is adequate when there are many games played, the results can be undesirable over short seasons. E.g., if a team wins all of its games, the MLE of its strength is infinite. This can be resolved with a Bayesian approach where a joint posterior probability distribution is deduced for the Bradley-Terry strengths. Such an application requires a choice of prior distribution for these strengths. While most authors have considered families of prior distributions which can reflect the experimenters' additional knowledge about the objects, for the application as a rating system, the different teams should be judged on equal terms. I will discuss some possible choices of prior distribution suitable for this application, as well as hierarchical models which leverage families of prior distributions, with examples from sports such as baseball, American football, and ice hockey.


Stochastisches Kolloquium:

Mittwoch, 30. Oktober 2019, 14:15 Uhr in Raum 903:

Hsien-Kuei Hwang (Academia Sinica, Taipei)

Stirling numbers of the second kind: the history of early developments and an elementary approach to asymptotic normality

A historical account is given of the early developments of the Stirling numbers of the second kind: in contrast to those in the West, those in the East, notably in Japan, have remained mostly unknown with the corresponding combinatorial origin traced back to at least 1600.
I will talk about the background, the mathematical developments in Japan in the Edo Period (1603--1868), and the corresponding developments in the West. Then after a brief survey on the various methods for proving the asymptotic normality N(n/log n, n/(log n)^2) of the Stirling numbers of the second kind, I will introduce a very simple, elementary approach to proving the local and central limit theorems. The approach, based on the principle of inclusion and exclusion and Stirling's formula for the factorial, is also applicable to several dozens of other examples in the literature and in the OEIS (Online Encyclopedia of Integer Sequences). This talk is based on joint works with Xiaoling Dou (Waseda University) and with Chong-Yi Li (Academia Sinica).


Oberseminar Stochastik:

Mittwoch, 16. Oktober 2019, Raum 711 gr

14:00 Uhr: Master-Abschlussvortrag Lucas Then

Cumulant-Covariances and their Application within Homogeneous Marked Poisson Process Models for Parallel Spike Trains

MathFinanceColloquium:

Montag, 02.09.2019, 17:15 Uhr, Raum 711 groß

Jiling Cao (Auckland University of Technology):
Inferring information from the S&P 500 and CBOE indices: The more the merrier ?

The Chicago Board Options Exchange (CBOE) updated the CBOE Volatility Index (VIX) in 2003 and further launched the CBOE Skew Index (SKEW) in 2011, in order to measure the 30-day risk-neutral volatility and skewness of the S&P 500 Index (SPX). In this work, we mainly compares the information extracted from the SPX and CBOE indices in terms of the SPX option pricing performance. Based on our analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while, the SKEW is very noisy and does not contain much important information for option prices.


Oberseminar Stochastik:

Mittwoch, 14. August 2019, Raum 711 gr

14:00 Uhr: Bachelor-Abschlussvortrag von Anna-Lena Weinel

Minima und Maxima einer verzweigenden Irrfahrt

15:00 Uhr: Bachelor-Abschlussvortrag von Jan Lukas Igelbrink 

Rekursive Baumprozesse: Endogenität und bivariate Eindeutigkeit
 

Rhein-Main Kolloquium Stochastik:

Freitag, 24. Mai 2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15:15 Roland Bauerschmidt (University of Cambridge): 

Dynamics of strongly correlated spin systems
I will discuss some results on the problem of understanding the long-time behaviour of Glauber and Kawasaki dynamics of spin systems in the regimes of strong correlations. This is joint work with Thierry Bodineau.

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 h Prof. Dr. Chiranjib Mukherjee (Universität Münster):

Gaussian multiplicative chaos in the Wiener space
In the classical finite dimensional setting, a Gaussian multiplicative chaos (GMC) is obtained by tilting an ambient measure by the exponential of a centred Gaussian field indexed by a domain in the Euclidean space. In the two-dimensional setting and when the underlying field is "log-correlated", GMC measures share close connection to the 2D Liouville quantum gravity, which has seen a lot of revived interest in the recent years.
A natural question is to construct a GMC in the infinite dimensional setting, where techniques based on log-correlated fields in finite dimensions are no longer available. In the present context, we consider a GMC on the classical Wiener space, driven by a (mollified) Gaussian space-time white noise. In $d\geq 3$, in a previous work with A. Shamov and O. Zeitouni, we showed that the total mass of this GMC, which is directly connected to the (smoothened) Kardar-Parisi-Zhang equation in $d\geq 3$, converges for small noise intensity to a well-defined strictly positive random variable, while for larger intensity (i.e. for small temperature) it collapses to zero. We will report on joint work with Yannic Bröker (Münster) where we study the endpoint distribution of a Brownian path under the GMC measure and show that, for low temperature, the endpoint GMC distribution localizes in few spatial islands and produces asymptotically purely atomic states.


Stochastisches Kolloquium:

Mittwoch, 8. Mai 2019, 14:15 Uhr in Raum 711 gr:

Christian Webb (Aalto/Finland)

An introduction to log-correlated fields and multiplicative chaos

Log-correlated fields are stochastic processes arising e.g. in various models of statistical mechanics, probabilistic combinatorics, and probabilistic number theory. They are characterized by having a logarithmic singularity in their covariance. Multiplicative chaos measures are random fractal measures built from these log-correlated fields. I will briefly discuss the precise definition of these objects, how multiplicative chaos measures can be used to study extreme values of log-correlated fields, and time permitting, how this type of results can be applied e.g. in random matrix theory.tba


Rhein-Main-Kolloquium Stochastik

Freitag, 02.02.2024, Raum 711 groß, Robert-Mayer-Straße 10

Sprecher: tba


Frankfurter Seminar

Mittwoch, 24.01.2024, Raum 711 groß und klein, Robert-Mayer-Straße 10


Frankfurter Seminar

Mittwoch, 22.11.2023, Raum 711 groß und klein, Robert-Mayer-Straße 10


Frankfurter Seminar

Mittwoch, 08.11.2023, Raum 711 groß und klein, Robert-Mayer-Straße 10


Oberseminar Stochastik

Mittwoch, 18.10.2023, in Präsenz, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Masterarbeit von Annika Meyer (Goethe Universität Frankfurt)

Title: tba

Rhein-Main-Kolloquium Stochastik

Freitag, 07.07.2023, Raum 711 groß, Robert-Mayer Straße 10

Sprecher: Prof. David Prömel (Uni Mannheim), 15:15 Uhr

Titel: Model-free portfolio theory: a rough path approach

Abstract: Classical approaches to optimal portfolio selection problems are based on probabilistic models for the asset returns or prices. However, by now it is well observed that the performance of optimal portfolios are highly sensitive to model misspecifications. To account for various type of model risk, robust and model-free approaches have gained more and more importance in portfolio theory. Using rough path theory, we provide a pathwise foundation for stochastic Ito integration, which covers most commonly applied trading strategies and mathematical models of financial markets possibly under model uncertainty. Based on this pathwise foundation, we develop a model-free approach to stochastic portfolio theory and Cover's universal portfolio. The use of rough path theory allows for treating significantly more general portfolios in a model-free setting, compared to previous model-free approaches.
The talk is based on joint works with Andrew Allan, Christa Cuchiero and Chong Liu.

Sprecher: Prof. Christoph Czichowsky (LSE), 16:45 Uhr

Titel: Hedging and portfolio optimisation in rough volatility models 

Abstract: Rough volatility models have become quite popular recently, as they capture both the fractional scaling of the time series of the historic volatility (Gatheral et al. 2018) and the behaviour of the implied volatility surface (Fukasawa 2011, Bayer et al. 2016) remarkably well. In contrast to classical stochastic volatility models, the volatility process is neither a Markov process nor a semimartingale. Therefore, these models fall outside the scope of standard stochastic analysis and provide new mathematical challenges. In this talk, we present an overview of of this new paradigm in volatility modelling and consider the impact of rough volatility on hedging and portfolio optimisation.The talk is based on joint works with David Martins, Johannes Muhle-Karbe and Denis Schelling.


Frankfurter Seminar

Mittwoch, 28.06.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Michael Joswig (TU Berlin)

Titel: tba


Frankfurter Seminar

Mittwoch, 07.06.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Carla Cederbaum (Universität Tübingen)

Titel: tba


Stochastisches Kolloquium

Mittwoch, 31.05.2023, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Prof. Wolfgang Woess (TU Graz)

Title: Boundary behaviour of branching Markov chains

Abstract: We study multi-type branching Markov chains on denumerable type spaces in discrete time. The way of thinking is in the sense that the type space carries a structure, e.g., of a graph with certain geometric properties to be specified, and that the population moves at random in space, so that the types are considered as sites. It is supposed that the offspring distributions satisfy a uniform "L log L" moment condition with type-independent expected offspring number, and that the associated "base" Markov chain on the space is transient and irreducible. Given the population at time n at the different sites, we normalize it by dividing by its total number. The resulting empirical distribution is a random probability measure on the type space. Assuming that the latter is equipped with  a "geometric" compactification with a boundary at infinity, a main focus is on the question whether the sequence of empirical distributions converges a.s. weakly to a random probability distribution on the boundary.

This is joint work with Vadim A. Kaimanovich (Ottawa), to appear in Ann. Inst. H. Poincaré Prob. Stat.


Frankfurter Seminar

Mittwoch, 10.05.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Renzo Cavalieri (Colorado State University, Fort Collins)

Titel: tba


Frankfurter Seminar

Mittwoch, 19.04.2023, Raum 711 groß und klein, Robert-Mayer Straße 10

16:45 Uhr: Jean-François Le Gall (Université Paris-Saclay)

Titel: Recent developments in random geometry


Oberseminar Stochastik

Mittwoch, 12.04.2023, in Präsenz, Raum 711 groß, Robert-Mayer Straße 10

14:15 Uhr: Fabian Roth (Goethe Universität Frankfurt)

Title: AlphaZero, Stochastic MuZero & Co: Strengths and limitations of state-of-the-art reinforcement learning algorithms that involve planning

Stochastisches Kolloquium

Mittwoch, 15.02.2023, Beginn 14.00 h, in Raum 711 groß.

14:00 Uhr: Dr. Charline Smadi (INRAE und Institut Fourier, Université Grenoble)

Titel: Quasi-equilibria and click times for a variant of Muller's ratchet

Abstract: We will introduce and study a variant of a well-known model in population genetics, named Muller's ratchet, which is seen as one explanation of the ubiquity of sexual selection in Nature. Consider a population of N individuals, each of them carrying a type in \N_0. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type k has the same selective advantage over all individuals with type k′>k, and type k mutates to type k+1 at a constant rate (in the classical Muller's ratchet, the selective advantage is proportional to k′−k). For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the click times of the ratchet (i.e. the times at which the hitherto minimal (`best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a ``dual'' hierarchical multitype logistic system. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations. 

This is a joint work with A. González Casanova and Anton Wakolbinger.


Stochastisches Kolloquium

Mittwoch, 25. Januar 2023, Raum 711 groß

14:15 Uhr: Prof. Dr. Noela Müller (TU Eindhoven)

Title: The rank of sparse symmetric matrices over arbitrary fields

Abstract: Let F be an arbitrary field and (G_{n,d/n})_n be a sequence of sparse weighted Erdős-Rényi random graphs on n vertices with edge probability d/n, whose edge weights are drawn from F \{0} according to a matrix J_n. We show that the normalised rank of the adjacency matrix of (G_{n,d/n})_n converges in probability to a constant, and derive the limiting expression. Our result shows that for the general class of sparse symmetric matrices under consideration, the asymptotics of the normalised rank are independent of the edge weights and even the field, in the sense that the limiting constant for the general case coincides with the one previously established for adjacency matrices of sparse (non-weighted) Erdős-Rényi matrices over R in the seminal work of Bordenave, Lelarge and Salez. Our proof, which is purely combinatorial in its nature, is based on an intricate adaptation of the novel perturbation method of Coja-Oghlan, Ergür, Gao, Hetterich and Rolvien to the symmetric setting.

This is joint work with Rem co van der Hofstad and Haodong Zhu.


Oberseminar Stochastik

Mittwoch, 18. Januar 2023, in Präsenz, Raum 711 groß 

14:15 Uhr: Simon Arendt (Goethe Universität Frankfurt)

Title: Austauschbare Arrays

Abstract: Der funktionale Darstellungssatz von Aldous-Hoover-Kallenberg verallgemeinert den Satz von de Finetti auf mehrdimensionale austauschbare Arrays. Im Vortrag wird der Spezialfall zwei-dimensionaler Arrays vorgestellt. Neben dem formalen Beweis diskutieren wir als praktische Anwendung die Implikationen des Darstellungssatzes für die Bayes-Statistik mit relationalen Daten.


Rhein-Main-Kolloquium Stochastik (in Präsenz)

Am Freitag, 13.01.2023, Raum 711 groß, Robert-Mayer Straße 10

Krankheitsbedingt entfällt leider der erste Vortrag von Herrn Dr. Hermann.
Der Beginn verändert sich auf 16.00 Uhr !

16.00 Uhr "Kaffeepause"

16.45 Uhr  Beginn des Vortrages von Herrn Dr. Marcel Ortgiese, (University of Bath)

Sprecher: Dr. Marcel Ortgiese (University of Bath)

Titel: “The contact process on tree-like graphs"

Abstract: The contact process is a simple model for the spread of an infection in a structured population. I will first survey some of the recent results for the contact process when the underlying graph is either a finite or infinite random graph that is locally tree-like. The main focus of the talk will be to understand what changes when the underlying graph also evolves over time. We will look both at the case when edges update independently of the infection, but also the dependent case. In the latter case, the random graph reacts to the infection by only resampling connections to neighbours that are infected. The main question we will answer is first of all whether the contact process exhibits a phase transition. If it does, we will look at how the phase transition depends on the underlying graph dynamics.


Oberseminar Stochastik

Mittwoch, 7. Dezember 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Tessa Feller (Goethe Universität Frankfurt)

Title: Neues zum Lemma von Johnson-Lindenstrauss


Oberseminar Stochastik

Mittwoch, 2. November 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Marie Kuhn (Goethe Universität Frankfurt)

Title: Modeling neuronal spike trains with Hawkes processes


Oberseminar Stochastik

Mittwoch, 19. Oktober 2022, in Präsenz, Raum 711 groß

14:15 Uhr: Jasper Ischebeck (Goethe Universität Frankfurt)

Rhein-Main-Kolloquium Stochastik (in Präsenz)

Freitag, 01.07.2022, Raum 711 groß, Robert-Mayer Straße 10

Dr. Julian Gerstenberg (Goethe Universität Frankfurt), 15:15 Uhr
Dr. Jonathan Warren (University of Warwick), 16:45 Uhr

Sprecher: Dr. Julian Gerstenberg
Titel: Functional Representation Theorems for Exchangeable Laws
Abstract: Functional Representation theorems (FRTs) for exchangeable random objects exist for many types of data structures, for example sequences (de Finetti/Hewitt-Savage), partitions (Kingman), hierarchical structures, graphs or more general array-like data structures (Aldous-Hoover-Kallenberg).  In this talk several known FRTs are presented and the language of category theory [vocabulary: cagegory, functor, natural transformation] is used to introduce an abstract concept of data structures, which allows for a unified formulation of many known FRTs. This leads to a conjecture about a "General FRT".  No knowledge of category theory is assumed to follow this talk, the concepts will be motivated by statistical practise. This research is funded by the DFG project 502386356. 

Sprecher: Dr. Jonathan Warren, Universty of Warwick
Titel: At the edge of a cloud of Brownian particles
Abstract: The talk concerns a model for the motion of particles carried in a turbulent fluid in which a single particle moves according to an SDE of the form dX_t= \sigma dB_t + dW(t,X_t). Here, W is a Gaussian field, describing the environment, and B is an independent Brownian motion representing some additional diffusivity. We are interested in the behaviour at large times, but far from the origin.  There,  we find a transition which is analogous to that between weak and strong disorder for polymer models, and at the transition the stochastic heat equation appears.



Oberseminar Stochastik:

Am Mittwoch, 29.06.2022, in Präsenz, Raum 711 groß, 14:15 Uhr

Philipp Klein (Magdeburg) 

Anomaly detection based on MOSUM statistics in large image data

Abstract:

Being able to identify anomalies in image data is important in many practical applications. This includes the detection of cancerous cells in medicine, obstacles in autonomous driving and fissures in the construction material of buildings. When the data is large, it is oftentimes helpful to have an efficient pre-processing procedure to identify areas potentially containing anomalies. This holds especially true when these anomalies are sparse.
We develop a procedure for the detection of fissures in 2D image data based on moving sum (MOSUM) statistics. In particular, based on the observation of local geometric properties of fissures and natural anomalies in concrete, we use a combination of moving semicircle- and 'rectangle'-shaped windows in order to identify regions that potentially have fissures. Under the null assumption of no anomalies for P-dimensional image data, we are able to show convergence for MOSUM statistics using a general class of scan windows fulfilling (weak) regularity conditions towards functionals of P-parameter Gaussian processes. In particular, this class includes 2D convex sets that we use for fissure detection.


Die Identifikation von Anomalien in Bilddaten ist in vielen praktischen Anwendungen von großer Bedeutung. Dazu zählen die Erkennung von Krebszellen, das Wahrnehmen von Hindernissen beim autonomen Fahren sowie die Detektion von Rissen in Baumaterial. Bei großen Datenmengen ist es oftmals hilfreich, ein effizientes Vorverarbeitungsverfahren zu haben, welches dabei hilft, mögliche Regionen mit Anomalien zu identifizieren. Dies trifft besonders dann zu, wenn die Anomalien nur einen sehr kleinen Teil des Datensatzes ausmachen. Mithilfe  so genannter 'moving sum' (MOSUM)-Statistiken entwickeln wir ein Verfahren zur Erkennung von Rissen in zweidimensionalen Daten. Basierend auf lokalen geometrischen Eigenschaften von Rissen und natürlichen Anomalien verwenden wir kreisförmige und 'rechteckige' Fenster zur Identifikation von Regionen, die möglicherweise Risse enthalten. Unter der Nullannahme der Nichtexistenz von Anomalien in P-dimensionalen Bilddaten zeigen wir schwache Konvergenz für MOSUM-Statistiken, die eine allgemeine Klassen von Scan-Fenstern verwendet, gegen Funktionale von P-Parameter Gaußprozessen. Diese Klasse beinhaltet insbesondere zweidimensionale konvexe Mengen, welche wir für die Risserkennung verwenden.


Am Mittwoch, 08.06.2022, in Präsenz, Raum 711 groß,

15:15 Uhr
Terence Tsui Ho Lung (Oxford)
Uncovering genealogy of superprocesses through lookdown constructions

Abstract: In this talk, I will demonstrate how one can uncover genealogical structures and ancestral lineages of spatially-structured population through the means of lookdown constructions. By enriching a spatially-structured population with levels imposed on individual particles that follows carefully selected dynamics, one can introduce a spatial-level Markovian population that enables us to trace the motion of ancestral lineages of the underlying spatial population. In particular, we study populations with a juvenile and adult stage, and show their many possible scaling limits with rich dynamics. Finally, we explain how we use a lookdown construction to derive the motion of ancestral lineages in these scaling limits.

16:30 Uhr
Adrian Martini (Oxford)
Modelling Aggregation and Dormancy in the Life Cycle of Dictyostelium discoideum

Abstract: The amoeba Dictyostelium discoideum transitions from unicellular to multicellular life when food is scarce. To avoid extinction, individuals aggregate, form complex fruiting bodies and disperse spores for new amoebae to hatch under favourable conditions. Additionally, spores may delay their hatching process in a phenomenon called dormancy. The population uses dormancy to reduce risk in the presence of environmental fluctuations.
We seek to understand the dynamics that lead to the formation of fruiting bodies and aim to quantify the spread of advantageous alleles under dormancy. In the first part of the talk, we replicate the formation of aggregates under the influence of noise by introducing an approximate Stochastic PDE. In the second part, we review recent results on dormancy and discuss possible extensions.

Berufspraxiskolloquium:

Am 23.6.22. (Do) um 18 c.t., Raum 711 groß, findet das nächste Berufspraxiskolloquium statt, zu dem alle Interessierten herzlich eingeladen sind. 

Vortragender: Dr. Patrick Liebrich (Emcore) 

Titel: Der Finanzplatz Liechtenstein

Zusammenfassung:

Das Fürstentum Liechtenstein bietet durch seine Lage in der Schweizer Zollunion und dem EWR hervorragende steuerliche und rechtliche Rahmenbedingungen. So ist der Kleinstaat Sitz vieler europäisch agierender Finanzdienstleister. Und doch unterscheidet sich die Art der hier ansässigen Unternehmen deutlich von denen in den grossen Finanzzentren wie Frankfurt. In dem Vortrag wird der Finanzplatz Liechtenstein mit seinen Besonderheiten vorgestellt.

Oberseminar Stochastik:

Mittwoch, 04. Mai 2022, in Präsenz, Raum 711 groß

14:15 Uhr:Masterarbeit von Marina Sturm:

Nichtparametrische Statistik zur Detektion von Richtungswechseln in Organellenbewegungen

Oberseminar Stochastik:

Mittwoch, 09. Februar 2022, via Zoom

14:15 Uhr: Solveig Plomer zum aktuellen Stand ihres Promotionsprojekts:

Detecting changes in movement direction and speed in cell organelles
 


Oberseminar Stochastik:

Mittwoch, 15. Dezember 2021, via Zoom

https://uni-frankfurt.zoom.us/j/97187235503?pwd=Njg5bTUxZlhQdmNJMHd0MUtxOFVHdz09

14:15 Uhr:  Masterarbeit von Herrn Robin Masic:

Methoden der Richtungsstatistik mit Anwendung auf Plastid-Bewegungen
 
 

 

Berufspraxiskolloquium:

Das Kolloquium richtet sich speziell an Studierende und soll Einblicke in spätere Berufsfelder geben. Es ist eine Kombination aus einer Firmenvorstellung und einem Vortrag über die Anwendung mathematischer Methoden in der Berufspraxis.

Am 9.12. (Do) um 18:15 (!) findet das nächste Berufspraxiskolloquium per Zoom statt, zu dem alle Interessierten herzlich eingeladen sind.

Referenten: Christian Braun und Nadine Mbenda (PricewaterhouseCoopers | Risk & Regulation)

Titel: Quantitatives Kreditrisikomanagement: Einführung und aktuelle Herausforderungen

Zusammenfassung: Das Credit Risk Quant-Team von PwC Deutschland wird die Dimensionen des Kreditrisikos, wesentliche Risikomodelle, die Ermittlung der Risikovorsorge unter IFRS 9 und die aktuellen Herausforderungen bei der Kreditrisikomodellierung vorstellen.

Herr Prof. Dr. Christoph Kühn lädt Sie zu diesem Zoom-Meeting ein.

Thema: Berufspraxiskolloquium
Uhrzeit: 9.Dez..2021 06:00 PM Amsterdam, Berlin, Rom, Stockholm, Wien

Zoom-Meeting beitreten
https://uni-frankfurt.zoom.us/j/95253176690?pwd=RmVoZ1RRWEhhU3hGQ3hocGdVT3VXUT09

Meeting-ID: 952 5317 6690
Kenncode: 772102


Rhein-Main-Kolloquium Stochastik:

 

 

Freitag, 03.12.2021 - via Zoom.

https://uni-frankfurt.zoom.us/j/93449699353?pwd=Wm5GNE90Qk90K0o0cjIxb3AvanFIUT09

Meeting ID: 934 4969 9353
Passcode: 828632

15:15-16:15: Nina Gantert (TU München)

16:15-16:45: (virtual) coffee break

16:45-17:45: Paolo Dai Pra (Università degli Studi di Verona)

Nina Gantert (TU München)

Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation

Abstract: We study the asymptotics of the k-regular self-similar fragmentation process. For α>0 and an integer k≥2, this is the Markov process (I_t)_{t≥0} in which each It is a union of open subsets of [0,1), and independently each subinterval of It of size u breaks into k equally sized pieces at rate u^α. Let k^{−mt} and k^{−Mt} be the respective sizes of the largest and smallest fragments in I_t. By relating (I_t)_{t≥0} to a branching random walk, we find that there exist explicit deterministic functions g(t) and h(t) such that |mt−g(t)|≤1 and |Mt−h(t)|≤1 for all sufficiently large t. Furthermore, for each n, we study the final time at which fragments of size k^{-n} exist. In particular, by relating our branching random walk to a certain point process, we show that, after suitable rescaling, the laws of these times converge to a Gumbel distribution as n→∞.

Based on joint work with Piotr Dyszewski, Samuel G. G. Johnston, Joscha Prochno and Dominik Schmid

Paolo Dai Pra (Università degli Studi di Verona)

Self-sustained oscillations in interacting systems: an overview and some recent advances

Abstract: Self organized collective periodic behavior is seen to emerge in several different contexts: from neuroscience to tectonic plates movements, from population dynamics to epidemiology. A large variety of stochastic models have been proposed to capture this phenomenon at a mathematical level, showing that it may be induced by a combination of factors including noise, dissipation, loss of Markovianity and/or of time reversibility. Most of the present literature concerns mean-field models, where the thermodynamic limit is well understood at a dynamical level, and the emergence of oscillations can be seen from the macroscopic evolution equations. In models with short range interaction it is much harder to understand how self organization at microscopic level may produce large scale rhythms. Some partial results have been obtained for a non-reversible modification of the nearest neighbour Ising model.


 

Berufspraxiskolloquium:

Das Kolloquium richtet sich speziell an Studierende und soll Einblicke in spätere Berufsfelder geben. Es ist eine Kombination aus einer Firmenvorstellung und einem Vortrag über die Anwendung mathematischer Methoden in der Berufspraxis.

Donnerstag den 28.10.2021 um 16:15 via Zoom

Dr. Klaus Rinne (Ernst & Young, FAAS Quant Team)

Titel: Valuation of interest rate options under negative rates
Table of Content: - Introduction to the concept of volatility - Interest rate cap & floor - Working as a quant at EY

Zoom-Meeting beitreten
https://uni-frankfurt.zoom.us/j/95253176690?pwd=RmVoZ1RRWEhhU3hGQ3hocGdVT3VXUT09

Meeting-ID: 952 5317 6690
Kenncode: 772102

Oberseminar Stochastik:

Dienstag, 27. Juli 2021, via ZOOM

https://uni-frankfurt.zoom.us/j/96877275138?pwd=azBCSGNKZTd4elBnT0lKNjhlWHVMUT09

Meeting-ID: 968 7727 5138
Kenncode: 322615

10:00 Uhr: Master-Abschlussvortrag von Niyat Isayas

Rekonstruktionsprobleme an rein zufälligen rekursiven Bäumen


 

Oberseminar Stochastik:

Mittwoch, 30. Juni 2021, via ZOOM

Zugangsdaten bitte über Apl. Prof. Dr. Gaby Schneider anfragen.

14:15 Uhr: Master-Abschlussvortrag Fabian Schneider

Ein multivariater Ansatz zur Analyse der Fütteraktivität von Bienen


MathFinanceColloquium/ Berufspraxiskolloquium:

Dienstag, 29.06.2021, 14:15 Uhr via ZOOM

Zugangsdaten bitte über Prof. Dr. Christoph Kühn anfragen.

Referenten:
Kasra Khani (Consultant, d-fine)
Dr. Hans-Peter Wächter (Partner, d-fine)

Titel:
The Endgame of Libor – Einstieg als Finanzmathematiker in einer Zeit voller Veränderungen

Beschreibung:
d-fine ist mit mehr als 1000 Mitarbeiterinnen und Mitarbeitern eines der führenden Beratungsunternehmen für quantitativ und technologisch anspruchsvolle Projekte. Nach einer Vorstellung der Firma möchten wir Ihnen gerne die Benchmark Reform im Rahmen von USA Studentenkrediten vorstellen. Unser Vortrag thematisiert hierbei insbesondere den Projektalltag und die besonderen Erfahrungen als Einsteiger in Zeiten der Pandemie.

Alle (theoretisch oder praktisch) Interessierten sind herzlich eingeladen!


Rhein-Main-Kolloquium Stochastik:

Freitag, 11.06.2021: ONLINE-Veranstaltung

Zoom access to the talks:

https://uni-frankfurt.zoom.us/j/94648348387?pwd=anVJNnJKY2NZTVBGZWR4UXdGRHpOUT09

Meeting ID: 946 4834 8387

Passcode: 969450

15:15-16:15: Gaultier Lambert (Zürich)

16:15-16:45: virtual coffee break

16:45-17:45: Christian Brennecke (Harvard)

Gaultier Lambert

Title: Normal approximation for traces of random unitary matrices

This talk aim to report on the fluctuations of traces of powers of a random n by n matrix U distributed according to the Haar measure on the unitary group. This classical random matrix problem has been extensively studied using several different methods such as asymptotics of Toeplitz determinants, representation theory, loop equations etc. It turns out that for any k≥1, Tr[U^k] converges as n tends to infinity to a Gaussian random variable with a super exponential rate of convergence. In this talk, I will explain some of these results and present some recent work with Kurt Johansson (KTH) in which we revisited this problem in a multivariate setting.

Christian Brennecke

Title: On the TAP equations for the Sherrington-Kirkpatrick Model

In this talk, I will review the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass and present a dynamical derivation, valid at sufficiently high temperature. In our derivation, the TAP equations follow as a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish decay of higher order correlation functions. We illustrate this by proving a suitable decay bound on the three point functions which implies an analogue of the TAP equations for the two point functions. The talk is based on joint work with A. Adhikari, P. von Soosten and H.T. Yau.


Stochastisches Kolloquium:

Freitag, 28. Mai 2021 via ZOOM

https://uni-frankfurt.zoom.us/j/95773112662?pwd=NVZFSG1tdytoQlpFSEtHUkxqTzBsQT09

Meeting-ID: 957 7311 2662

Kenncode: 548086

15:15 Uhr: Vortrag von Dr. Jon Warren Department of Statistics, University of Warwick

A family of local times studied as a Markov process

Abstract

 

Oberseminar Stochastik:

Mittwoch, 05. Mai 2021, via ZOOM

https://uni-frankfurt.zoom.us/j/94756581976?pwd=ejZFQjdhRG5GaEdMaDdvM3p3aUY3UT09

Meeting ID: 947 5658 1976
Passcode: 223308

14:30 Uhr: Master-Abschlussvortrag Insea Schlattmeier

Überleben und Wachstum von Parasitenpopulationen in räumlich strukturierten Wirtspopulationen

Oberseminar Stochastik:

Mittwoch, 24. März 2021, via ZOOM

Zugangsdaten bitte über Prof. Dr. Wakolbinger anfragen

14:30 Uhr: Master-Abschlussvortrag Jan Lukas Igelbrink

Langreichweitige Seedbank-Koaleszenten und fraktionale Brownbewegungen


 

Rhein-Main-Kolloquium Stochastik:

Freitag, 29.01.2021: ONLINE-Veranstaltung

Zoom access to the talks:
https://uni-frankfurt.zoom.us/j/91292915620?pwd=QkR5THI0MklWWDR1ajBoUytFOXBwUT09

Meeting-ID: 912 9291 5620
Code: 109618

15:15-16:15: Gabor Lugosi (Pompeu Fabra University, Barcelona)

16:15-16:45: virtual coffee break

16:45-17:45: Po-Ling Loh (University of Cambridge)

Gábor Lugosi

Title: Root finding and broadcasting in random recursive trees

Abstract: Uniform and preferential attachment trees are among the simplest examples of dynamically growing networks. The statistical problems we address in this talk regard discovering the past of the tree when a present-day snapshot is observed. We present a few results that show that, even in gigantic networks, a lot of information is preserved from the very early days. In particular, we discuss the problem of finding the root and the broadcasting problem.


Po-Ling Loh

Title: Statistical inference for infectious disease modeling

Abstract: We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. Furthermore, we prove that the confidence sets are almost surely persistent, i.e., they settle down after a finite number of time steps. In the second scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test.

This is joint work with Justin Khim and Varun Jog.


Oberseminar Stochastik:

Mittwoch, 16. Dezember 2020, VidyoConnect

Zugangsdaten bitte über Prof. Dr. Neininger anfragen

14:15 Uhr: Master-Abschlussvortrag Ân Hòang

Zur Struktur zufälliger Permutationen, GEM- und Poisson-Dirichlet-Verteilungen


Oberseminar Stochastik:

Mittwoch, 14. Oktober 2020

14:15 Uhr: Master-Abschlussvortrag Denis Spiegel

Convergence Rates in Distributional Reinforcement Learning

Rhein-Main-Kolloquium Stochastik:

Freitag, 29.05.2020: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Giada Basile (Universität Rom): Titel tba

16.15-16.45 Uhr Kaffeepause

16.15 Uhr (tba)

Stochastisches Kolloquium:

Mittwoch, 22. Januar 2020, 14:15 Uhr in Raum 711 gr

14:00 Uhr: Vortrag von Dr. Charline Smadi, Universität Grenoble

Crossing a fitness valley as a metastable transition in a stochastic population model
We consider a stochastic model of population dynamics where each individual is characterised by a trait in {0,1,...,L} and has a natural reproduction rate, a logistic death rate due to age or competition, and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is an  exponentially distributed random variable.

This is a joint work with Anton Bovier and Loren Coquille


Stochastisches Kolloquium:

Mittwoch, 18. Dezember 2019, 14:15 Uhr in Raum 711 gr

14:00 Uhr: Vortrag von Maurice Georgi

Stochastische Modellierung von segmentweisen linearen Plastidbewegungen


Rhein-Main-Kolloquium Stochastik:

Freitag, 06.12.2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Simone Warzel (TU München): Quantum spin glasses: a mathematical challenge

The theory of classical mean-field spin glasses is a well-established and celebrated field within probability theory. The addition of a constant perpendicular magnetic field introduces a non-commuting term into the energy of such spin glasses and hence causes quantum effects. The main aim of this talk is to give an overview over some of the motivations for the study of quantum spin glasses. I will also review some first mathematical results in this field. Among them is a derivation of the key features of the thermal phase diagram of the simplest of all mean-field spin glasses, the quantum random energy model.

16.15-16.45 Uhr Kaffeepause

16.15 Uhr Matthias Erbar (Bonn): A variational characterization of the Sine_ß point process

The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_ß process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine_ß process. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional. Joint work with Martin Huesmann and Thomas Leblé 

 

MathFinanceColloquium/ Berufspraxiskolloquium:

Donnerstag, 05.12.2019, 16:15 Uhr, Raum 711 groß

Dr. Jürgen Bierbaum (Alte Leipziger Versicherung): Bewertung in unvollständigen Märkten - Finanzmathematik in der Lebensversicherung

Die Mehrzahl der Lebensversicherungsverträge in Deutschland enthält langfristige Zinsgarantien. Die Preisfindung sowie die ökonomische und bilanzielle Bewertung dieser Verträge erfordert die Entwicklung komplexer finanz- und versicherungsmathematischer Modelle. Wegen der Illiquidität der Märkte für langfristige Kapitalanlagen ist auch die Kalibrierung der Bewertungsmodelle eine nichttriviale Aufgabe. Zusätzlich sollte bereits beim Produktdesign auf eine kapitaleffiziente Struktur der Verpflichtungen geachtet werden. Im Vortrag werden einige wichtige Aufgabenstellungen aus der Praxis sowie gängige Ansätze zu ihrer Lösung vorgestellt.

Im Anschluss ist eine kurze Nachsitzung im Frankfurt and Friends geplant.


Gastvortrag:

Montag, 18. November um 12:30 Uhr in Raum 110

Sprecher: Prof. Dr. Dirk Metzler, FB Biologie, LMU München

Hybridzone zwischen Rabenkrähen und Nebelkrähen: Artbildung allein durch Paarungspräferenzen?

Aaskrähen gibt es in zwei Farbmorphen: in Westeuropa als schwarze Rabenkrähen und in Nord-, Ost-, und Südeuropa als grau-schwarz-gemusterte Nebelkrähen. Wo die Verbreitungsgebiete der beiden Farbmorphen an einader grenzen,z.B. in Deutschland an der Elbe, kommt es zur Hybridisierung. Die Krähen scheinen jedoch Verpaarung innerhalb ihrer jeweiligen Farbmorphe zu bevorzugen. Mittels mathematischer Modellierung und numerischen Simulationen untersuchen wir, ob solche assortativen Paarungspräferenzen eine stabile Koexistenz der beiden Farbmorphen erklären kann und eventuell zur Aufspaltung der Aaskrähen in zwei Arten führen wird. Wir passen unser Modell an populationsgenetische Daten an und berücksichtigen die genetische Architektur der Gefiederfärbung. Eine überraschende Vorhersage unserer Modellierung ist, dass die Hybridzone einer räumlichen Dynamik unterliegt, die stark davon abhängt, wie zwei Genloci für die Ausprägung der Gefiederfärbung interagieren. (Kooperation mit Jochen Wolf, Joshua Penalba und Ulrich Knief)
 

Stochastisches Kolloquium:

Mittwoch, 13. November 2019, Raum 711 gr

14:00 Uhr: Vortrag von Prof. Dr. John T Whelan (School of Mathematical Sciences (Statistics), Rochester Institute of Technology and Institute for Theoretical Physics)

Bayesian Applications of the Bradley-Terry Model to Sports Team Ratings

The Bradley-Terry-Zermelo model has been widely used to evaluate paired comparison experiments, with applications ranging from taste tests to rating chess players. In this model, each object being compared has a strength parameter, and the probability of winning a comparison is proportional to this strength. I consider the application of this model to the problem of rating or ranking teams based on their game results when the schedule is not balanced. While the traditional maximum-likelihood implementation is adequate when there are many games played, the results can be undesirable over short seasons. E.g., if a team wins all of its games, the MLE of its strength is infinite. This can be resolved with a Bayesian approach where a joint posterior probability distribution is deduced for the Bradley-Terry strengths. Such an application requires a choice of prior distribution for these strengths. While most authors have considered families of prior distributions which can reflect the experimenters' additional knowledge about the objects, for the application as a rating system, the different teams should be judged on equal terms. I will discuss some possible choices of prior distribution suitable for this application, as well as hierarchical models which leverage families of prior distributions, with examples from sports such as baseball, American football, and ice hockey.


Stochastisches Kolloquium:

Mittwoch, 30. Oktober 2019, 14:15 Uhr in Raum 903:

Hsien-Kuei Hwang (Academia Sinica, Taipei)

Stirling numbers of the second kind: the history of early developments and an elementary approach to asymptotic normality

A historical account is given of the early developments of the Stirling numbers of the second kind: in contrast to those in the West, those in the East, notably in Japan, have remained mostly unknown with the corresponding combinatorial origin traced back to at least 1600.
I will talk about the background, the mathematical developments in Japan in the Edo Period (1603--1868), and the corresponding developments in the West. Then after a brief survey on the various methods for proving the asymptotic normality N(n/log n, n/(log n)^2) of the Stirling numbers of the second kind, I will introduce a very simple, elementary approach to proving the local and central limit theorems. The approach, based on the principle of inclusion and exclusion and Stirling's formula for the factorial, is also applicable to several dozens of other examples in the literature and in the OEIS (Online Encyclopedia of Integer Sequences). This talk is based on joint works with Xiaoling Dou (Waseda University) and with Chong-Yi Li (Academia Sinica).


Oberseminar Stochastik:

Mittwoch, 16. Oktober 2019, Raum 711 gr

14:00 Uhr: Master-Abschlussvortrag Lucas Then

Cumulant-Covariances and their Application within Homogeneous Marked Poisson Process Models for Parallel Spike Trains

MathFinanceColloquium:

Montag, 02.09.2019, 17:15 Uhr, Raum 711 groß

Jiling Cao (Auckland University of Technology):
Inferring information from the S&P 500 and CBOE indices: The more the merrier ?

The Chicago Board Options Exchange (CBOE) updated the CBOE Volatility Index (VIX) in 2003 and further launched the CBOE Skew Index (SKEW) in 2011, in order to measure the 30-day risk-neutral volatility and skewness of the S&P 500 Index (SPX). In this work, we mainly compares the information extracted from the SPX and CBOE indices in terms of the SPX option pricing performance. Based on our analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while, the SKEW is very noisy and does not contain much important information for option prices.


Oberseminar Stochastik:

Mittwoch, 14. August 2019, Raum 711 gr

14:00 Uhr: Bachelor-Abschlussvortrag von Anna-Lena Weinel

Minima und Maxima einer verzweigenden Irrfahrt

15:00 Uhr: Bachelor-Abschlussvortrag von Jan Lukas Igelbrink 

Rekursive Baumprozesse: Endogenität und bivariate Eindeutigkeit
 

Rhein-Main Kolloquium Stochastik:

Freitag, 24. Mai 2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15:15 Roland Bauerschmidt (University of Cambridge): 

Dynamics of strongly correlated spin systems
I will discuss some results on the problem of understanding the long-time behaviour of Glauber and Kawasaki dynamics of spin systems in the regimes of strong correlations. This is joint work with Thierry Bodineau.

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 h Prof. Dr. Chiranjib Mukherjee (Universität Münster):

Gaussian multiplicative chaos in the Wiener space
In the classical finite dimensional setting, a Gaussian multiplicative chaos (GMC) is obtained by tilting an ambient measure by the exponential of a centred Gaussian field indexed by a domain in the Euclidean space. In the two-dimensional setting and when the underlying field is "log-correlated", GMC measures share close connection to the 2D Liouville quantum gravity, which has seen a lot of revived interest in the recent years.
A natural question is to construct a GMC in the infinite dimensional setting, where techniques based on log-correlated fields in finite dimensions are no longer available. In the present context, we consider a GMC on the classical Wiener space, driven by a (mollified) Gaussian space-time white noise. In $d\geq 3$, in a previous work with A. Shamov and O. Zeitouni, we showed that the total mass of this GMC, which is directly connected to the (smoothened) Kardar-Parisi-Zhang equation in $d\geq 3$, converges for small noise intensity to a well-defined strictly positive random variable, while for larger intensity (i.e. for small temperature) it collapses to zero. We will report on joint work with Yannic Bröker (Münster) where we study the endpoint distribution of a Brownian path under the GMC measure and show that, for low temperature, the endpoint GMC distribution localizes in few spatial islands and produces asymptotically purely atomic states.


Stochastisches Kolloquium:

Mittwoch, 8. Mai 2019, 14:15 Uhr in Raum 711 gr:

Christian Webb (Aalto/Finland)

An introduction to log-correlated fields and multiplicative chaos

Log-correlated fields are stochastic processes arising e.g. in various models of statistical mechanics, probabilistic combinatorics, and probabilistic number theory. They are characterized by having a logarithmic singularity in their covariance. Multiplicative chaos measures are random fractal measures built from these log-correlated fields. I will briefly discuss the precise definition of these objects, how multiplicative chaos measures can be used to study extreme values of log-correlated fields, and time permitting, how this type of results can be applied e.g. in random matrix theory.tba

 


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