{
  "id": "math/9901118",
  "version": "v1",
  "published": "1999-01-26T16:02:18.000Z",
  "updated": "1999-01-26T16:02:18.000Z",
  "title": "On the distribution of the length of the second row of a Young diagram under Plancherel measure",
  "authors": [
    "Jinho Baik",
    "Percy Deift",
    "Kurt Johansson"
  ],
  "comment": "25 pages, AMS-LaTex file",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "nlin.SI",
    "solv-int"
  ],
  "abstract": "We investigate the probability distribution of the length of the second row of a Young diagram of size $N$ equipped with Plancherel measure. We obtain an expression for the generating function of the distribution in terms of a derivative of an associated Fredholm determinant, which can then be used to show that as $N\\to\\infty$ the distribution converges to the Tracy-Widom distribution [TW] for the second largest eigenvalue of a random GUE matrix. This paper is a sequel to [BDJ], where we showed that as $N\\to\\infty$ the distribution of the length of the first row of a Young diagram, or equivalently, the length of the longest increasing subsequence of a random permutation, converges to the Tracy-Widom distribution [TW] for the largest eigenvalue of a random GUE matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-01-26T16:02:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "young diagram",
      "second row",
      "plancherel measure",
      "random gue matrix",
      "tracy-widom distribution"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......1118B"
    }
  }
}