{
  "id": "2005.13961",
  "version": "v1",
  "published": "2020-05-28T13:00:17.000Z",
  "updated": "2020-05-28T13:00:17.000Z",
  "title": "On the joint moments of the characteristic polynomials of random unitary matrices",
  "authors": [
    "Theodoros Assiotis",
    "Jonathan P. Keating",
    "Jon Warren"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a real-valued random variable that plays an important role in the ergodic decomposition of the Hua-Pickrell measures. This enables us to establish connections between the characteristic function of this random variable and the $\\sigma$-Painlev\\'{e} III' equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-28T13:00:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random unitary matrix",
      "characteristic polynomial",
      "joint moments",
      "general real values",
      "asymptotic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}