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Bibliographic Details
Main Author: Sun, Maxwell
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2406.07597
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author Sun, Maxwell
author_facet Sun, Maxwell
contents 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 $\text{des}(w) + \text{des}(w^{-1})$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_07597
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups
Sun, Maxwell
Combinatorics
Probability
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 $\text{des}(w) + \text{des}(w^{-1})$ 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.
title A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups
topic Combinatorics
Probability
url https://arxiv.org/abs/2406.07597