{
  "id": "1010.4595",
  "version": "v2",
  "published": "2010-10-21T22:48:45.000Z",
  "updated": "2011-04-16T10:24:49.000Z",
  "title": "Asymptotic normality of the size of the giant component via a random walk",
  "authors": [
    "Bela Bollobas",
    "Oliver Riordan"
  ],
  "comment": "11 pages; slightly expanded, reference added",
  "journal": "J. Combinatorial Theory B 102 (2012), 53--61",
  "doi": "10.1016/j.jctb.2011.04.003",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of $G(n,p)$ above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp's exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-16T10:24:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "giant component",
      "asymptotic normality",
      "random walk",
      "martingale arguments",
      "study karps exploration process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4595B"
    }
  }
}