{
  "id": "1005.3231",
  "version": "v2",
  "published": "2010-05-18T15:38:18.000Z",
  "updated": "2010-05-19T11:05:59.000Z",
  "title": "A class of even walks and divergence of high moments of large Wigner random matrices",
  "authors": [
    "O. Khorunzhiy"
  ],
  "comment": "version 2: minor changes; formulas (1.4) and (2.2) corrected",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study high moments of truncated Wigner nxn random matrices by using their representation as the sums over the set W of weighted even closed walks. We construct the subset W' of W such that the corresponding sum diverges in the limit of large n and the number of moments proportional to n^{2/3} for any truncation of the order n^{1/6+epsilon}, epsilon>0 provided the probability distribution of the matrix elements is such that its twelfth moment does not exist. This allows us to put forward a hypothesis that the finiteness of the twelfth moment represents the necessary condition for the universal upper bound of the high moments of large Wigner random matrices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-19T11:05:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "large wigner random matrices",
      "twelfth moment",
      "truncated wigner nxn random matrices",
      "divergence",
      "study high moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.3231K"
    }
  }
}