A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups

2024/06/11 by Sun, Maxwell
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2406.07597

Abstract

The Mallows distribution is a non-uniform distribution, first introduced over permutations to study non-ranked data, in which permutations are weighted according to their length. It can be generalized to any Coxeter group, and we study the distribution of des(w) + des(w^-1) where w is a Mallows distributed element of a finite irreducible Coxeter group. We show that the asymptotic behavior of this statistic is Guassian. The proof uses a size-bias coupling with Stein's method.

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