The Mallows measure is a probability measure on $$S_n$$Sn where the probability of a permutation $$\pi $$π is proportional to $$q^{l(\pi )}$$ql(π) with $$q > 0$$q>0 being a parameter and $$l(\pi )$$l(π) the number of inversions in $$\pi $$π. We show the convergence of the random empirical measure of the product of two independent permutations drawn from the Mallows measure, when q is a function of n and $$n(1-q)$$n(1-q) has limit in $$\mathbb {R}$$R as $$n \rightarrow \infty $$n→∞.

中文翻译：

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两个独立锦葵排列的乘积的经验测度的极限

Mallows 测度是对 $$S_n$$Sn 的概率测度，其中置换 $$\pi $$π 的概率与 $$q^{l(\pi )}$$ql(π) 成正比q > 0$$q>0 是一个参数，$$l(\pi )$$l(π) 是 $$\pi $$π 中的反演次数。当 q 是 n 的函数并且 $$n(1-q)$$n(1-q) 在 $ 中有限制时，我们展示了从 Mallows 度量中得出的两个独立排列的乘积的随机经验度量的收敛性$\mathbb {R}$$R 为 $$n \rightarrow \infty $$n→∞。