On the length of the longest common subsequence of two independent Mallows permutations

Abstract

The Mallows measure is a probability measure on Sn where the probability of a permutation π is proportional to q l(π) with q > 0 being a parameter and l(π) the number of inversions in π. We prove three weak laws of large numbers and a central limit theorem for the length of the longest common subsequences of two independent permutations drawn from the Mallows measure for different regimes of the parameter q.