The Annals of Applied Probability

The length of the longest common subsequence of two independent mallows permutations

Ke Jin

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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 $n\to\infty$.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 3 (2019), 1311-1355.

Dates
Received: July 2017
First available in Project Euclid: 19 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1550566832

Digital Object Identifier
doi:10.1214/17-AAP1351

Mathematical Reviews number (MathSciNet)
MR3914546

Zentralblatt MATH identifier
07057456

Subjects
Primary: 60F05: Central limit and other weak theorems 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 05A05: Permutations, words, matrices

Keywords
Longest common subsequence longest increasing subsequence Mallows measure

Citation

Jin, Ke. The length of the longest common subsequence of two independent mallows permutations. Ann. Appl. Probab. 29 (2019), no. 3, 1311--1355. doi:10.1214/17-AAP1351. https://projecteuclid.org/euclid.aoap/1550566832


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