{
  "id": "1304.7589",
  "version": "v2",
  "published": "2013-04-29T08:17:01.000Z",
  "updated": "2014-07-04T19:09:04.000Z",
  "title": "Limit shapes of bumping routes in the Robinson-Schensted correspondence",
  "authors": [
    "Dan Romik",
    "Piotr Śniady"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson-Schensted algorithm is applied to a finite sequence of independent, identically distributed random variables with the uniform distribution $U[0,1]$ on the unit interval, followed by an insertion of a deterministic number $\\alpha$. The bumping route converges after scaling, in the limit as the length of the sequence tends to infinity, to an explicit, deterministic curve depending only on $\\alpha$. This extends our previous result on the asymptotic determinism of Robinson-Schensted insertion, and answers a question posed by Moore in 2006.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-04T19:09:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68Q87",
      "60C05",
      "05E10",
      "20C30"
    ],
    "keywords": [
      "robinson-schensted correspondence",
      "asymptotic shape",
      "finite sequence",
      "identically distributed random variables",
      "limit shape theorem describing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7589R"
    }
  }
}