{
  "id": "1307.5645",
  "version": "v3",
  "published": "2013-07-22T10:13:39.000Z",
  "updated": "2016-09-01T08:21:24.000Z",
  "title": "Robinson-Schensted-Knuth algorithm, jeu de taquin and Kerov-Vershik measures on infinite tableaux",
  "authors": [
    "Piotr Śniady"
  ],
  "comment": "42 pages. Version 2: change of title, minor changes. Version 3: bibliography has been updated, the figures which in version 2 were not displayed properly have been repaired",
  "journal": "SIAM J. Discrete Math. 28 (2014), no. 2, 598-630",
  "doi": "10.1137/130930169",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We investigate Robinson-Schensted-Knuth algorithm (RSK) and Sch\\\"utzenberger's jeu de taquin in the infinite setup. We show that the recording tableau in RSK defines an isomorphism of the following two dynamical systems: (i) a sequence of i.i.d. random letters equipped with Bernoulli shift, and (ii) a random infinite Young tableau (with the distribution given by Vershik-Kerov measure, corresponding to some Thoma character of the infinite symmetric group) equipped with jeu de taquin transformation. As a special case we recover the results on non-colliding random walks and multidimensional Pitman transform.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-19T12:33:53.000Z",
      "comment": "42 pages version 2: change of title, minor changes"
    },
    {
      "version": "v3",
      "updated": "2016-09-01T08:21:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05E10",
      "20C30",
      "20C32",
      "37A05"
    ],
    "keywords": [
      "robinson-schensted-knuth algorithm",
      "kerov-vershik measures",
      "infinite tableaux",
      "random infinite young tableau",
      "multidimensional pitman transform"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5645S"
    }
  }
}