A central limit theorem for the two-sided descent statistic on Coxeter groups
arXiv:1908.07955 · doi:10.37236/10744
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, Özdemir and Röttger.
21 pages incl. appendix