On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations
Baik, Jinho ; Deift, Percy ; Johansson, Kurt
arXiv, 9810105 / Harvested from arXiv
Text on arXiv
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 $l_N$.
Publié le : 1998-10-16
Classification:  Mathematics - Combinatorics,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  05A05, 15A52, 33D45, 45E05, 60F99 
@article{9810105,
     author = {Baik, Jinho and Deift, Percy and Johansson, Kurt},
     title = {On the Distribution of the Length of the Longest Increasing Subsequence
  of Random Permutations},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9810105}
}

Baik, Jinho; Deift, Percy; Johansson, Kurt. On the Distribution of the Length of the Longest Increasing Subsequence
  of Random Permutations. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9810105/