{
  "id": "1505.06700",
  "version": "v1",
  "published": "2015-05-25T17:41:50.000Z",
  "updated": "2015-05-25T17:41:50.000Z",
  "title": "Bulk eigenvalue statistics for random regular graphs",
  "authors": [
    "Roland Bauerschmidt",
    "Jiaoyang Huang",
    "Antti Knowles",
    "Horng-Tzer Yau"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We consider the uniform random $d$-regular graph on $N$ vertices, with $d \\in [N^\\alpha, N^{2/3-\\alpha}]$ for arbitrary $\\alpha > 0$. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian Orthogonal Ensemble.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T17:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C50",
      "60B20",
      "15B52"
    ],
    "keywords": [
      "random regular graphs",
      "bulk eigenvalue statistics",
      "local eigenvalue correlation functions",
      "consecutive eigenvalues coincide",
      "uniform random"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506700B"
    }
  }
}