{
  "id": "1911.10591",
  "version": "v1",
  "published": "2019-11-24T18:53:23.000Z",
  "updated": "2019-11-24T18:53:23.000Z",
  "title": "Large deviations for the largest eigenvalue of sub-Gaussian matrices",
  "authors": [
    "Fanny Augeri",
    "Alice Guionnet",
    "Jonathan Husson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. We estimate the probability that the largest eigenvalue is close to some value large enough and show that if the entries do not have sharp sub-Gaussian tails, the rate function is strictly smaller than the rate function for Gaussian entries. This contrasts with \\cite{HuGu} where it was shown that the law of the largest eigenvalue of Wigner matrices with entries with sharp sub-Gaussian tails obeys a large deviation principle with the same rate function than in the Gaussian case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-24T18:53:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "largest eigenvalue",
      "sub-gaussian matrices",
      "rate function",
      "sharp sub-gaussian tails obeys",
      "wigner matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}