{
  "id": "1804.11340",
  "version": "v1",
  "published": "2018-04-30T17:40:54.000Z",
  "updated": "2018-04-30T17:40:54.000Z",
  "title": "Local laws for polynomials of Wigner matrices",
  "authors": [
    "Laszlo Erdos",
    "Torben Kruger",
    "Yuriy Nemish"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have constant variance. Under some numerically checkable conditions, we establish the optimal local law, i.e., we show that the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-30T17:40:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "46L54",
      "15B52"
    ],
    "keywords": [
      "wigner matrices",
      "general self-adjoint polynomials",
      "independent random matrices",
      "optimal local law",
      "free probability theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}