For Mallows permutations, the longest common subsequence of two independent copies satisfies a central limit theorem for fixed parameters and an L^p law of large numbers with constant sqrt(6)/3 when the parameters approach 1 with n(1-q) -> infinity.
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Limit Theorems for the Length of the Longest Common Subsequence of Mallows Permutations
For Mallows permutations, the longest common subsequence of two independent copies satisfies a central limit theorem for fixed parameters and an L^p law of large numbers with constant sqrt(6)/3 when the parameters approach 1 with n(1-q) -> infinity.