{
  "id": "0908.1982",
  "version": "v4",
  "published": "2009-08-13T21:15:50.000Z",
  "updated": "2010-01-11T22:08:06.000Z",
  "title": "Random matrices: Universality of local eigenvalue statistics up to the edge",
  "authors": [
    "Terence Tao",
    "Van Vu"
  ],
  "comment": "24 pages, no figures, to appear, Comm. Math. Phys. One new reference added",
  "categories": [
    "math.PR"
  ],
  "abstract": "This is a continuation of our earlier paper on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in that paper from the bulk of the spectrum up to the edge. In particular, we prove a variant of the universality results of Soshnikov for the largest eigenvalues, assuming moment conditions rather than symmetry conditions. The main new technical observation is that there is a significant bias in the Cauchy interlacing law near the edge of the spectrum which allows one to continue ensuring the delocalization of eigenvectors.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-01-11T22:08:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52"
    ],
    "keywords": [
      "local eigenvalue statistics",
      "wigner random matrices",
      "assuming moment conditions",
      "earlier paper",
      "universality results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-010-1044-5",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Sep",
      "volume": 298,
      "number": 2,
      "pages": 549
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.298..549T"
    }
  }
}