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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... (Update)
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BibTeX entry: (Update)
J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, Preprint, math.CO/9810105. http://citeseer.ist.psu.edu/article/baik99distribution.html More
@article{ baik99distribution,
author = "Baik and Deift and Johansson",
title = "On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations",
journal = "JAMS: Journal of the American Mathematical Society",
volume = "12",
year = "1999",
url = "citeseer.ist.psu.edu/article/baik99distribution.html" }
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