{
  "id": "1702.01281",
  "version": "v1",
  "published": "2017-02-04T12:19:08.000Z",
  "updated": "2017-02-04T12:19:08.000Z",
  "title": "Benjamini-Schramm convergence and limiting eigenvalue density of random matrices",
  "authors": [
    "Sergio Andraus"
  ],
  "comment": "8pages, 2 figures. Proceedings paper for the Probability Theory Symposium 2016 held at RIMS, Kyoto University, on Dec. 19-22 2016. To be published on RIMS K\\^oky\\uroku",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We review the application of the notion of local convergence on locally finite randomly rooted graphs, known as Benjamini-Schramm convergence, to the calculation of the global eigenvalue density of random matrices from the beta-Gaussian and beta-Laguerre ensembles. By regarding a random matrix as the weighted adjacency matrix of a graph, and choosing the root of such a graph with uniform probability, one can use the Benjamini-Schramm limit to produce the spectral measure of the adjacency operator of the limiting graph. We illustrate how the Wigner semicircle law and the Marchenko-Pastur law are obtained from this machinery.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-04T12:19:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix",
      "limiting eigenvalue density",
      "benjamini-schramm convergence",
      "finite randomly rooted graphs",
      "global eigenvalue density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}