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

摘要

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 R as n -> infinity.