The Length of the Longest Increasing Subsequence of a Random Mallows Permutation

Carl Mueller and Shannon Starr ()
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Carl Mueller: University of Rochester
Shannon Starr: University of Rochester

Journal of Theoretical Probability, 2013, vol. 26, issue 2, 514-540

Abstract: Abstract The Mallows measure on the symmetric group S n is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is a positive parameter and the number of inversions of π is equal to the number of pairs i π j . We prove a weak law of large numbers for the length of the longest increasing subsequence for Mallows distributed random permutations, in the limit that n→∞ and q→1 in such a way that n(1−q) has a limit in R.

Keywords: Random; permutations; 60B15; 82B05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0364-5

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