{
  "id": "1811.00064",
  "version": "v1",
  "published": "2018-10-31T18:57:46.000Z",
  "updated": "2018-10-31T18:57:46.000Z",
  "title": "A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions",
  "authors": [
    "Estelle Basor",
    "Pavel Bleher",
    "Robert Buckingham",
    "Tamara Grava",
    "Alexander Its",
    "Elizabeth Its",
    "Jonathan P. Keating"
  ],
  "comment": "39 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "nlin.SI"
  ],
  "abstract": "We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the sigma-Painleve V equation. The derivation involves the analysis of a formula for the joint moments in terms of a determinant of generalised Laguerre polynomials using the Riemann-Hilbert method. We use this connection with the sigma-Painleve V equation to derive explicit formulae for the joint moments and to show that in the large-matrix limit the joint moments are related to a solution of the sigma-Painleve III equation. Using the conformal block expansion of the tau-functions associated with the sigma-Painleve V and the sigma-Painleve III equations leads to general conjectures for the joint moments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-31T18:57:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "joint moments",
      "cue characteristic polynomials",
      "painleve functions",
      "sigma-painleve",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}