{
  "id": "math/9810105",
  "version": "v2",
  "published": "1998-10-16T17:29:53.000Z",
  "updated": "1999-03-26T17:54:09.000Z",
  "title": "On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations",
  "authors": [
    "Jinho Baik",
    "Percy Deift",
    "Kurt Johansson"
  ],
  "comment": "60 pages, 14 figures, AMS-LaTeX, typo correstions, new references",
  "journal": "J. Amer. Math. Soc. 12 (1999), no. 4, 1119--1178",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "nlin.SI",
    "solv-int"
  ],
  "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 $l_N$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-03-26T17:54:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "15A52",
      "33D45",
      "45E05",
      "60F99"
    ],
    "keywords": [
      "longest increasing subsequence",
      "random permutation",
      "distribution function",
      "random gue matrix",
      "steepest decent method"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....10105B"
    }
  }
}