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

Maxwell Sun

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

Combinatorics 2024-06-13 v1 Probability

Authors: Maxwell Sun

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 $\text{des}(w) + \text{des}(w^{-1})$ 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.

Keywords

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Cite

@article{arxiv.2406.07597,
  title  = {A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups},
  author = {Maxwell Sun},
  journal= {arXiv preprint arXiv:2406.07597},
  year   = {2024}
}

Comments

49 pages, 1 figure. arXiv admin note: text overlap with arXiv:2005.09802 by other authors

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

Abstract

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