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

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

2011-02-16

arxiv.org/abs/1102.3402v2

Mathematics

Probability

Scientific paper

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 $\pi$ is equal to the number of pairs $i \pi_j$. 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 $n$ tends to infinity and $q$ tends to 1 in such a way that $n(1-q)$ has a limit in $\R$.

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