A central limit theorem for the two-sided descent statistic on Coxeter groups
Combinatorics
2022-02-04 v2 Group Theory
Probability
Abstract
We study the asymptotic behaviour of the statistic (des+ides) which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of its inverse. Our main result is a central limit theorem for the probability distributions associated to this statistic. This answers a question of Kahle-Stump and generalises work of Chatterjee-Diaconis, \"Ozdemir and R\"ottger.
Cite
@article{arxiv.1908.07955,
title = {A central limit theorem for the two-sided descent statistic on Coxeter groups},
author = {Benjamin Brück and Frank Röttger},
journal= {arXiv preprint arXiv:1908.07955},
year = {2022}
}
Comments
21 pages incl. appendix