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.
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Brück et al. (2022) studied this question.
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