{
  "id": "1106.4366",
  "version": "v3",
  "published": "2011-06-22T04:18:00.000Z",
  "updated": "2013-04-18T23:39:34.000Z",
  "title": "Large Deviations for Random Matrices",
  "authors": [
    "Sourav Chatterjee",
    "S. R. S. Varadhan"
  ],
  "comment": "13 pages. Appeared in Comm. on Stochastic Analysis, vol. 6 no. 1, 1-13, 2012",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We prove a large deviation result for a random symmetric n x n matrix with independent identically distributed entries to have a few eigenvalues of size n. If the spectrum S survives when the matrix is rescaled by a factor of n, it can only be the eigenvalues of a Hilbert-Schmidt kernel k(x,y) on [0,1] x [0,1]. The rate function for k is $I(k)=1/2\\int h(k(x,y) dxdy$ where h is the Cramer rate function for the common distribution of the entries that is assumed to have a tail decaying faster than any Gaussian. The large deviation for S is then obtained by contraction.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-18T23:39:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrices",
      "large deviation result",
      "cramer rate function",
      "independent identically distributed entries",
      "tail decaying faster"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4366C"
    }
  }
}