{
  "id": "1309.1975",
  "version": "v2",
  "published": "2013-09-08T16:38:54.000Z",
  "updated": "2014-02-07T06:36:58.000Z",
  "title": "Expansion in finite simple groups of Lie type",
  "authors": [
    "Emmanuel Breuillard",
    "Ben Green",
    "Robert Guralnick",
    "Terence Tao"
  ],
  "comment": "78 pages, 2 figures. This is the final version, incorporating referee comments",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper, establishing strongly dense subgroups in simple algebraic groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-07T06:36:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G40",
      "20N99"
    ],
    "keywords": [
      "finite simple groups",
      "lie type",
      "simple algebraic groups",
      "random cayley graphs",
      "establishing strongly dense subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 78,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1975B"
    }
  }
}