{
  "id": "1506.04012",
  "version": "v1",
  "published": "2015-06-12T13:13:14.000Z",
  "updated": "2015-06-12T13:13:14.000Z",
  "title": "No-gaps delocalization for general random matrices",
  "authors": [
    "Mark Rudelson",
    "Roman Vershynin"
  ],
  "comment": "45 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $\\ell_2$ norm. Our results pertain to a wide class of random matrices, including matrices with independent entries, symmetric and skew-symmetric matrices, as well as some other naturally arising ensembles. The matrices can be real and complex; in the latter case we assume that the real and imaginary parts of the entries are independent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-12T13:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "random matrix",
      "general random matrices",
      "no-gaps delocalization",
      "imaginary parts",
      "high probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150604012R"
    }
  }
}