{
  "id": "2002.06455",
  "version": "v1",
  "published": "2020-02-15T21:52:38.000Z",
  "updated": "2020-02-15T21:52:38.000Z",
  "title": "The Exponential of the S^1 Trace of the Free Field and Verblunsky Coefficients",
  "authors": [
    "Mohammad Latifi",
    "Doug Pickrell"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "An identity of Szego, and a volume calculation, heuristically suggest a simple expression for the distribution of Verblunsky coefficients with respect to the (normalized) exponential of the $S^1$ trace of the Gaussian free field. This heuristic expression is incorrect. We show that what we believe to be the correct formula is equivalent to a family of combinatorial identities (for moments of measures) which are of intrinsic interest and which are relatively easy to check empirically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-15T21:52:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "verblunsky coefficients",
      "exponential",
      "gaussian free field",
      "intrinsic interest",
      "volume calculation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}