The Limit of the Empirical Measure of the Product of Two Independent Mallows Permutations

Abstract

The Mallows measure is a probability measure on $S_n$ where the probability of a permutation $\pi$ is proportional to $q^{l(\pi )}$ with $q>0$ being a parameter and $l(\pi )$ the number of inversions in $\pi$. 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 $n(1-q)$ has limit in $\mathbb{R}$ as $n\to \infty$.

This article was previously a part of arXiv:1611.03840v1, which was subsequently split into this and what became arXiv:1611.03840v2 UPDATE: Version 2 of this article is uploaded by mistake, which is another article

References in corpus (1)

• Fixed points and cycle structure of random permutations

Cited by in corpus (2)

• The Length of the Longest Common Subsequence of Two Independent Mallows Permutations
• Limit Theorems for the Length of the Longest Common Subsequence of Mallows Permutations