{
  "id": "1901.07479",
  "version": "v1",
  "published": "2019-01-22T17:28:39.000Z",
  "updated": "2019-01-22T17:28:39.000Z",
  "title": "Mixed moments of characteristic polynomials of random unitary matrices",
  "authors": [
    "Emma C. Bailey",
    "Sandro Bettin",
    "Gordon Blower",
    "J. Brian Conrey",
    "Andrei Prokhorov",
    "Michael O. Rubinstein",
    "Nina C. Snaith"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.NT"
  ],
  "abstract": "Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-22T17:28:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "11M06"
    ],
    "keywords": [
      "random unitary matrices",
      "characteristic polynomial",
      "mixed moment",
      "painleve differential equation",
      "unitary group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}