Geodesic
A central limit theorem for the two-sided descent statistic on Coxeter groups
Benjamin Brück1 ; Frank Röttger2
1ETH Zürich
2University of Geneva
The electronic journal of combinatorics, Tome 29 (2022) no. 1
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We study the asymptotic behaviour of the statistic $(\operatorname{des}+\operatorname{ides})_W$ which assigns to an element $w$ of a finite Coxeter group $W$ the number of descents of $w$ plus the number of descents of $w^{-1}$. Our main result is a central limit theorem for the probability distributions associated to this statistic. This answers a question of Kahle-Stump and builds upon work of Chatterjee-Diaconis, Özdemir and Röttger.
DOI : 10.37236/10744
Classification : 20F55, 05A15, 05A16, 60F05

Benjamin Brück  1   ; Frank Röttger  2

1 ETH Zürich
2 University of Geneva 
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     author = {Benjamin Br\"uck and Frank R\"ottger},
     title = {A central limit theorem for the two-sided descent statistic on {Coxeter} groups},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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Benjamin Brück; Frank Röttger. A central limit theorem for the two-sided descent statistic on Coxeter groups. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10744

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