{
  "id": "math/0609806",
  "version": "v1",
  "published": "2006-09-28T14:22:39.000Z",
  "updated": "2006-09-28T14:22:39.000Z",
  "title": "Meixner polynomials and random partitions",
  "authors": [
    "Alexei Borodin",
    "Grigori Olshanski"
  ],
  "comment": "AMSTeX, 27 pages, to appear in Moscow Mathematical Journal",
  "journal": "Moscow Mathematical Journal 4 (2006), no. 4, 629-655.",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov's Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional lattice. In the particular case of z-measures, the correlation kernel of this process, called the discrete hypergeometric kernel, has especially nice properties. The aim of the paper is to derive the discrete hypergeometric kernel by a new method, based on a relationship between the z-measures and the Meixner orthogonal polynomial ensemble. The present paper can be viewed as an introduction to another our paper where the same approach is applied to studying a dynamical model related to the z-measures (Markov processes on partitions, Prob. Theory Rel. Fields 135 (2006), 84-152; arXiv: math-ph/0409075).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-28T14:22:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60G55",
      "33C45"
    ],
    "keywords": [
      "meixner polynomials",
      "random partitions",
      "discrete hypergeometric kernel",
      "z-measures",
      "okounkovs schur measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9806B"
    }
  }
}