{
  "id": "1608.04513",
  "version": "v1",
  "published": "2016-08-16T08:16:38.000Z",
  "updated": "2016-08-16T08:16:38.000Z",
  "title": "Asymptotics of orthogonal polynomials and the Painlevé transcendents",
  "authors": [
    "Dan Dai"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of this article, we list several open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-16T08:16:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E17",
      "34M55",
      "41A60"
    ],
    "keywords": [
      "orthogonal polynomials",
      "transcendents",
      "deift-zhous nonlinear steepest descent method",
      "applying deift-zhous nonlinear steepest descent",
      "review asymptotic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}