{
  "id": "1404.2096",
  "version": "v1",
  "published": "2014-04-08T11:54:40.000Z",
  "updated": "2014-04-08T11:54:40.000Z",
  "title": "On central limit theorems in the random connection model",
  "authors": [
    "Tim van de Brug",
    "Ronald Meester"
  ],
  "comment": "17 pages, 3 figures",
  "journal": "Phys. A 332 (2004), no. 1-4, 263-278",
  "doi": "10.1016/j.physa.2003.10.003",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a sequence of Poisson random connection models (X_n,lambda_n,g_n) on R^d, where lambda_n / n^d \\to lambda > 0 and g_n(x) = g(nx) for some non-increasing, integrable connection function g. Let I_n(g) be the number of isolated vertices of (X_n,lambda_n,g_n) in some bounded Borel set K, where K has non-empty interior and boundary of Lebesgue measure zero. Roy and Sarkar [Phys. A 318 (2003), no. 1-2, 230-242] claim that (I_n(g) - E I_n(g)) / \\sqrt Var I_n(g) converges in distribution to a standard normal random variable. However, their proof has errors. We correct their proof and extend the result to larger components when the connection function g has bounded support.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-08T11:54:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "central limit theorems",
      "poisson random connection models",
      "lebesgue measure zero",
      "standard normal random variable",
      "integrable connection function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2004,
      "month": "Feb",
      "volume": 332,
      "pages": 263
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004PhyA..332..263V"
    }
  }
}