Thomas Kahle: Limit theorems for permutation statistics

Abstract.

It has been long known that the number of descents of a random uniform permutation satisfies a central limit theorem when the size of the permutation group grows. We survey some new limit theorems, where for example, descents are replaced by more interesting statistics, or the permutation group is replaced by a finite Coxeter group, or instead of a central limit theorem, one proves a Gumbel limit of an extreme value statistics.