{
  "id": "1504.05170",
  "version": "v1",
  "published": "2015-04-20T19:43:45.000Z",
  "updated": "2015-04-20T19:43:45.000Z",
  "title": "Bulk universality of sparse random matrices",
  "authors": [
    "Jiaoyang Huang",
    "Benjamin Landon",
    "Horng-Tzer Yau"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the adjacency matrix of the ensemble of Erd\\H{o}s-R\\'enyi random graphs which consists of graphs on $N$ vertices in which each edge occurs independently with probability $p$. We prove that in the regime $pN \\gg 1$ these matrices exhibit bulk universality in the sense that both the averaged $n$-point correlation functions and distribution of a single eigenvalue gap coincide with those of the GOE. Our methods extend to a class of random matrices which includes sparse ensembles whose entries have different variances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-20T19:43:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sparse random matrices",
      "bulk universality",
      "single eigenvalue gap coincide",
      "point correlation functions",
      "methods extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}