{
  "id": "2112.12093",
  "version": "v2",
  "published": "2021-12-22T17:52:45.000Z",
  "updated": "2022-03-31T20:53:08.000Z",
  "title": "Small deviation estimates for the largest eigenvalue of Wigner matrices",
  "authors": [
    "László Erdős",
    "Yuanyuan Xu"
  ],
  "comment": "Minor update",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-31T20:53:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60B20"
    ],
    "keywords": [
      "largest eigenvalue",
      "wigner matrices",
      "precise right-tail small deviation estimates",
      "establish precise right-tail small deviation",
      "complex hermitian matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}