{
  "id": "1311.0984",
  "version": "v1",
  "published": "2013-11-05T08:07:38.000Z",
  "updated": "2013-11-05T08:07:38.000Z",
  "title": "The asymptotic size of the largest component in random geometric graphs with some applications",
  "authors": [
    "Ge Chen",
    "Chang-Long Yao",
    "Tian-De Guo"
  ],
  "comment": "22 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "For the size of the largest component in a supercritical random geometric graph, this paper estimates its expectation which tends to a polynomial on a rate of exponential decay, and sharpens its asymptotic result with a central limit theory. Similar results can be obtained for the size of biggest open cluster, and for the number of open clusters of percolation on a box, and so on.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-05T08:07:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "largest component",
      "asymptotic size",
      "applications",
      "central limit theory",
      "biggest open cluster"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0984C"
    }
  }
}