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June 2019 The length of the longest common subsequence of two independent mallows permutations
Ke Jin
Ann. Appl. Probab. 29(3): 1311-1355 (June 2019). DOI: 10.1214/17-AAP1351

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 $n\to\infty$.

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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

Information

Received: 1 July 2017; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057456
MathSciNet: MR3914546
Digital Object Identifier: 10.1214/17-AAP1351

Subjects:
Primary: 05A05, 60B15, 60F05

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2019
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