{
  "id": "1502.07983",
  "version": "v1",
  "published": "2015-02-27T17:40:20.000Z",
  "updated": "2015-02-27T17:40:20.000Z",
  "title": "Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails",
  "authors": [
    "Fanny Augeri"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a large deviation principle for the largest eigenvalue of Wigner matrices without Gaussian tails, namely such that the distribution tails $\\mathbb{P}( |X_{1,1}|>t)$ and $\\mathbb{P}(|X_{1,2}|>t)$ behave like $e^{-bt^{\\alpha}}$ and $e^{-at^{\\alpha}}$ respectively for some $a,b\\in (0,+\\infty)$ and $\\alpha\\in (0,2)$. The large deviation principle is of speed $N^{\\alpha/2}$ and with an explicit good rate function depending only on the tail distribution of the entries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-27T17:40:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations principle",
      "largest eigenvalue",
      "wigner matrices",
      "gaussian tails",
      "large deviation principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150207983A"
    }
  }
}