{
  "id": "1301.2915",
  "version": "v2",
  "published": "2013-01-14T10:33:52.000Z",
  "updated": "2013-01-15T11:25:10.000Z",
  "title": "Moderate deviations for the determinant of Wigner matrices",
  "authors": [
    "Hanna Döring",
    "Peter Eichelsbacher"
  ],
  "comment": "20 pages, one missing reference added; Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics and Statistics, 2013",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish a moderate deviations principle (MDP) for the log-determinant $\\log | \\det (M_n) |$ of a Wigner matrix $M_n$ matching four moments with either the GUE or GOE ensemble. Further we establish Cram\\'er--type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-15T11:25:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60F10",
      "15A18"
    ],
    "keywords": [
      "wigner matrices",
      "non-hermitian gaussian random matrices",
      "establish cramer-type moderate deviations",
      "moderate deviations principle",
      "goe ensemble"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}