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On the central limit theorem for the two-sided descent statistics in Coxeter groups


Féray, Valentin (2020). On the central limit theorem for the two-sided descent statistics in Coxeter groups. Electronic Communications in Probability, 25:online.

Abstract

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups Wn for which the two-sided descent statistics on a uniform random element of Wn is asymptotically normal. Recently, Brück and Röttger provided an almost-complete answer, assuming some regularity condition on the sequence Wn. 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).

Abstract

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups Wn for which the two-sided descent statistics on a uniform random element of Wn is asymptotically normal. Recently, Brück and Röttger provided an almost-complete answer, assuming some regularity condition on the sequence Wn. 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).

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 January 2020
Deposited On:17 Dec 2020 14:23
Last Modified:18 Dec 2020 21:02
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/20-ecp309
Official URL:https://projecteuclid.org/euclid.ecp/1585620028

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