{
  "id": "0905.4176",
  "version": "v2",
  "published": "2009-05-26T11:45:41.000Z",
  "updated": "2009-10-20T21:22:56.000Z",
  "title": "Bulk Universality for Wigner Matrices",
  "authors": [
    "Laszlo Erdos",
    "Sandrine Peche",
    "Jose A. Ramirez",
    "Benjamin Schlein",
    "Horng-Tzer Yau"
  ],
  "comment": "23 pages, 1 figure. An error in the previous version has been corrected",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider $N\\times N$ Hermitian Wigner random matrices $H$ where the probability density for each matrix element is given by the density $\\nu(x)= e^{- U(x)}$. We prove that the eigenvalue statistics in the bulk is given by Dyson sine kernel provided that $U \\in C^6(\\RR)$ with at most polynomially growing derivatives and $\\nu(x) \\le C e^{- C |x|}$ for $x$ large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-20T21:22:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "82B44"
    ],
    "keywords": [
      "wigner matrices",
      "bulk universality",
      "hermitian wigner random matrices",
      "wigner semicircle law",
      "dyson sine kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4176E"
    }
  }
}