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 prove a weak law of large numbers for the length of the longest common subsequences 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 $n\to\infty$.
Citation
Ke Jin. "The length of the longest common subsequence of two independent mallows permutations." Ann. Appl. Probab. 29 (3) 1311 - 1355, June 2019. https://doi.org/10.1214/17-AAP1351
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