{
  "id": "1904.07518",
  "version": "v1",
  "published": "2019-04-16T07:56:31.000Z",
  "updated": "2019-04-16T07:56:31.000Z",
  "title": "Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations",
  "authors": [
    "Walter Van Assche"
  ],
  "comment": "48 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics and probability and many other disciplines. In these notes we give an introduction to the use of orthogonal polynomials in random matrix theory, we explain the notion of multiple orthogonal polynomials, and we show the link with certain non-linear difference and differential equations known as Painlev\\'e equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-16T07:56:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "42C05",
      "60B20",
      "33E17"
    ],
    "keywords": [
      "multiple orthogonal polynomials",
      "random matrix theory",
      "painleve equations",
      "differential equations",
      "interesting special functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}