Translator Disclaimer
2020 On the central limit theorem for the two-sided descent statistics in Coxeter groups
Valentin Féray
Electron. Commun. Probab. 25: 1-6 (2020). DOI: 10.1214/20-ECP309

Abstract

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups $W_{n}$ for which the two-sided descent statistics on a uniform random element of $W_{n}$ is asymptotically normal. Recently, Brück and Röttger provided an almost-complete answer, assuming some regularity condition on the sequence $W_{n}$. In this note, we provide a shorter proof of their result, which does not require any regularity condition. The main new proof ingredient is the use of the second Wasserstein distance on probability distributions, based on the work of Mallows (Ann. Math. Statist., 1972).

Citation

Download Citation

Valentin Féray. "On the central limit theorem for the two-sided descent statistics in Coxeter groups." Electron. Commun. Probab. 25 1 - 6, 2020. https://doi.org/10.1214/20-ECP309

Information

Received: 9 December 2019; Accepted: 13 March 2020; Published: 2020
First available in Project Euclid: 31 March 2020

zbMATH: 1434.60041
MathSciNet: MR4089735
Digital Object Identifier: 10.1214/20-ECP309

Subjects:
Primary: 05E15, 60C05, 60F05

JOURNAL ARTICLE
6 PAGES


SHARE
Back to Top