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We study the asymptotic behaviour of the statistic (des+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.
Brück et al. (Fri,) studied this question.