论文标题
木棍置换及其倒数的中心限制定理
A central limit theorem for descents of a Mallows permutation and its inverse
论文作者
论文摘要
本文研究了排列$ w $中的下降$ \ des（w）$的渐近分布，并根据木棍措施分布。摩洛斯测量是针对研究排名数据引入的排列的一种不均匀的概率度量。在此度量下，根据其包含的反转数量对排列进行加权，并由参数$ Q $控制加权。主要结果是$ \ des（w）+\ des（w^{ - 1}）$的浆果定理，以及$（\ des（w），\ des（w^{ - 1}）$的联合中心限制定理，均为bivariate for a bivariate for，依赖于$ q $ q $。该证明使用Stein的方法与大小偏置耦合以及与木匠测量相关的再生过程。
This paper studies the asymptotic distribution of descents $\des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform probability measure on permutations introduced to study ranked data. Under this measure, permutations are weighted according to the number of inversions they contain, with the weighting controlled by a parameter $q$. The main results are a Berry-Esseen theorem for $\des(w)+\des(w^{-1})$ as well as a joint central limit theorem for $(\des(w),\des(w^{-1}))$ to a bivariate normal with a non-trivial correlation depending on $q$. The proof uses Stein's method with size-bias coupling along with a regenerative process associated to the Mallows measure.
