{
  "id": "math/0611369",
  "version": "v2",
  "published": "2006-11-13T07:35:07.000Z",
  "updated": "2008-10-01T05:15:08.000Z",
  "title": "Subcritical regimes in the Poisson Boolean model of continuum percolation",
  "authors": [
    "Jean-Baptiste Gouéré"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AOP352 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 4, 1209-1220",
  "doi": "10.1214/07-AOP352",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if $E(R^d)$ is finite, where $R$ denotes the radius of the balls around Poisson points and $d$ denotes the dimension. We also give related results concerning the integrability of the diameter of subcritical clusters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-01T05:15:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60D05",
      "82B43"
    ],
    "keywords": [
      "poisson boolean model",
      "continuum percolation",
      "subcritical regimes",
      "poisson points",
      "subcritical phase"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11369G"
    }
  }
}