{
  "id": "1201.1862",
  "version": "v2",
  "published": "2012-01-09T18:13:17.000Z",
  "updated": "2012-01-31T18:54:48.000Z",
  "title": "Localization and delocalization of eigenvectors for heavy-tailed random matrices",
  "authors": [
    "Charles Bordenave",
    "Alice Guionnet"
  ],
  "comment": "54 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider an n x n Hermitian random matrix with, above the diagonal, independent entries with alpha-stable symmetric distribution and 0 < alpha < 2. We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as n goes to infinity. When 1 < alpha < 2 we give vanishing bounds on the Lp-norm of the eigenvectors normalized to have unit L2-norm goes to 0. On the contrary, when 0 < alpha < 2/3, we prove that these eigenvectors are localized.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-31T18:54:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60B20",
      "60F15",
      "60E07"
    ],
    "keywords": [
      "heavy-tailed random matrices",
      "eigenvectors",
      "delocalization",
      "hermitian random matrix",
      "alpha-stable symmetric distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1862B"
    }
  }
}