{
  "id": "1111.5492",
  "version": "v1",
  "published": "2011-11-23T13:47:31.000Z",
  "updated": "2011-11-23T13:47:31.000Z",
  "title": "Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime",
  "authors": [
    "Maria Shcherbina",
    "Brunello Tirozzi"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue statistics converges in distribution to a Gaussian random variable with zero mean and variance which coincides with \"non gaussian\" part of the Wigner ensemble variance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-23T13:47:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52",
      "02.50.Ng",
      "02.10.Ox",
      "02.10.Ud",
      "02.10.Yn"
    ],
    "keywords": [
      "large random graphs",
      "central limit theorem",
      "diluted regime",
      "fluctuations",
      "linear eigenvalue statistics converges"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3698291",
      "journal": "Journal of Mathematical Physics",
      "year": 2012,
      "month": "Apr",
      "volume": 53,
      "number": 4,
      "pages": 3501
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53d3501S"
    }
  }
}