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• W2952954554 abstract "The authors consider the length, $l_N$, of the length of the longest increasing subsequence of a random permutation of $N$ numbers. The main result in this paper is a proof that the distribution function for $l_N$, suitably centered and scaled, converges to the Tracy-Widom distribution [TW1] of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest decent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 [DZ1] in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel [Ge] for the Poissonization of the distribution function of $l_N$." @default.
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• W2952954554 date "1998-10-16" @default.
• W2952954554 modified "2023-10-01" @default.
• W2952954554 title "On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations" @default.
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