{
  "id": "0806.0252",
  "version": "v1",
  "published": "2008-06-02T11:04:27.000Z",
  "updated": "2008-06-02T11:04:27.000Z",
  "title": "Susceptibility in subcritical random graphs",
  "authors": [
    "Svante Janson",
    "Malwina J. Luczak"
  ],
  "comment": "28 pages",
  "doi": "10.1063/1.2982848",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study the evolution of the susceptibility in the subcritical random graph $G(n,p)$ as $n$ tends to infinity. We obtain precise asymptotics of its expectation and variance, and show it obeys a law of large numbers. We also prove that the scaled fluctuations of the susceptibility around its deterministic limit converge to a Gaussian law. We further extend our results to higher moments of the component size of a random vertex, and prove that they are jointly asymptotically normal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-02T11:04:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05",
      "60F05"
    ],
    "keywords": [
      "subcritical random graph",
      "susceptibility",
      "deterministic limit converge",
      "random vertex",
      "precise asymptotics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Physics",
      "year": 2008,
      "month": "Dec",
      "volume": 49,
      "number": 12,
      "pages": 125207
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMP....49l5207J"
    }
  }
}