Philipp Dörr
Extreme Values of Permutation Statistics in Suitable Triangular Arrays
Two important statistics on random permutations are the number of inversions and the number of descents. These statistics can be generalized to Coxeter groups, where inversions and descents are defined with respect to a specific system of generators.The question of under which conditions these statistics satisfy a central limit theorem is well-understood. In contrast to that, the extremal type behavior of such statistics is rather unexplored yet. As the considered random permutation statistics only take finitely many values, we need to consider a suitably scaled triangular array of these statistics on groups of growing rank and tackle the dependencies therein.