{
  "id": "1410.0939",
  "version": "v1",
  "published": "2014-10-03T18:51:07.000Z",
  "updated": "2014-10-03T18:51:07.000Z",
  "title": "The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phase",
  "authors": [
    "Christian Webb"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, the absolute value of the characteristic polynomial (and suitable powers of it) converges in law to a Gaussian multiplicative chaos measure (for complex powers the convergence is to a random distribution).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-03T18:51:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random unitary matrix",
      "characteristic polynomial",
      "haar distributed random unitary matrices",
      "gaussian multiplicative chaos measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0939W"
    }
  }
}