A central limit theorem for descents of a Mallows permutation and its inverse

This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to Mallows measure. The measure is non-uniform probability on permutations introduced study ranked data. Under this measure, are weighted number inversions they contain, with weighting controlled by parameter $q$. main results Berry-Esseen theorem for $\des(w)+\des(w^{-1})$ as well joint central limit $(\des(w),\des(w^{-1}))$ bivariate normal non-trivial correlation depending proof uses Stein's method size-bias coupling along regenerative process associated