On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations
| dc.creator | Baik, Jinho | |
| dc.creator | Deift, Percy | |
| dc.creator | Johansson, Kurt | |
| dc.date | 1998-10-16 | |
| dc.date | 1999-03-26 | |
| dc.date.accessioned | 2026-07-07T05:26:30Z | |
| dc.date.available | 2026-07-07T05:26:30Z | |
| dc.description | 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 $l_N$. | |
| dc.description | 60 pages, 14 figures, AMS-LaTeX, typo correstions, new references | |
| dc.identifier | https://arxiv.org/abs/math/9810105 | |
| dc.identifier | http://arxiv.org/abs/math/9810105 | |
| dc.identifier | J. Amer. Math. Soc. 12 (1999), no. 4, 1119--1178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77570 | |
| dc.subject | Combinatorics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 05A05, 15A52, 33D45, 45E05, 60F99 | |
| dc.title | On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations | |
| dc.type | text |