{
  "id": "1306.2887",
  "version": "v2",
  "published": "2013-06-12T16:37:53.000Z",
  "updated": "2014-10-10T20:20:18.000Z",
  "title": "Delocalization of eigenvectors of random matrices with independent entries",
  "authors": [
    "Mark Rudelson",
    "Roman Vershynin"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that an n by n random matrix G with independent entries is completely delocalized. Suppose the entries of G have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high probability all unit eigenvectors of G have all coordinates of magnitude O(n^{-1/2}), modulo logarithmic corrections. This comes a consequence of a new, geometric, approach to delocalization for random matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-12T16:37:53.000Z",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-10T20:20:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "random matrices",
      "independent entries",
      "delocalization",
      "uniform tail decay",
      "modulo logarithmic corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2887R"
    }
  }
}