{
  "id": "1903.08304",
  "version": "v1",
  "published": "2019-03-20T01:17:06.000Z",
  "updated": "2019-03-20T01:17:06.000Z",
  "title": "Riemann--Hilbert Problems",
  "authors": [
    "Percy Deift"
  ],
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP"
  ],
  "abstract": "These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev\\'{e} equations and orthogonal polynomials, in solving the inverse scattering problem for certain integrable systems, and in proving universality for certain classes of random matrix ensembles. These lectures highlight a few such applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-20T01:17:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann-hilbert problems",
      "nonlinear steepest descent",
      "random matrix ensembles",
      "orthogonal polynomials",
      "method finds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}