{
  "id": "1806.01831",
  "version": "v1",
  "published": "2018-06-05T17:39:49.000Z",
  "updated": "2018-06-05T17:39:49.000Z",
  "title": "Multiplicative chaos and the characteristic polynomial of the CUE: the $L^1$-phase",
  "authors": [
    "Miika Nikula",
    "Eero Saksman",
    "Christian Webb"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian multiplicative chaos measure once correctly normalized. We prove this in the whole $L^1$- or subcritical phase of the chaos measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-05T17:39:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic polynomial",
      "haar distributed random unitary matrix",
      "distributed random unitary matrix converge",
      "gaussian multiplicative chaos measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}