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

2019/11/25 by Valentin Féray, Féray, Valentin
Mathematics · #05E15 #60C05 #60F05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1911.10939

openalex publication_date 2019/11/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In 2018, Kahle and Stump raised the following problem: identify sequences of\nfinite Coxeter groups W_n for which the two-sided descent statistics on a\nuniform random element of W_n is asymptotically normal. Recently, Br "uck and\nR "ottger provided an almost-complete answer, assuming some regularity\ncondition on the sequence W_n. In this note, we provide a shorter proof of\ntheir result, which does not require any regularity condition. The main new\nproof ingredient is the use of the second Wasserstein distance on probability\ndistributions, based on the work of Mallows (1972).\n

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