A central limit theorem for the two-sided descent statistic on Coxeter groups

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, Ozdemir and Rottger.