{
  "id": "math/0107056",
  "version": "v3",
  "published": "2001-07-06T23:18:57.000Z",
  "updated": "2003-01-31T14:44:46.000Z",
  "title": "Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram",
  "authors": [
    "Andrei Okounkov",
    "Nikolai Reshetikhin"
  ],
  "comment": "35 pages, 7 figures, to appear in JAMS",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.PR",
    "nlin.SI"
  ],
  "abstract": "Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. Our first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process. This general result is then applied to a particular specialization of the Schur process, namely to random 3-dimensional Young diagrams. The local geometry of a large random 3-dimensional diagram is described in terms of a determinantal point process on a 2-dimensional lattice with the incomplete beta function kernel (which generalizes the discrete sine kernel). A brief discussion of the universality of this answer concludes the paper.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-01-31T14:44:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schur process",
      "correlation function",
      "local geometry",
      "young diagram",
      "nice contour integral representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7056O"
    }
  }
}