{
  "id": "1010.5338",
  "version": "v2",
  "published": "2010-10-26T09:10:17.000Z",
  "updated": "2011-07-10T11:52:43.000Z",
  "title": "Percolation in the vacant set of Poisson cylinders",
  "authors": [
    "Johan Tykesson",
    "David Windisch"
  ],
  "comment": "29 pages, 3 figures",
  "journal": "Probability Theory and Related Fields, Volume 154, Issue 1 (2012), Page 165-191",
  "doi": "10.1007/s00440-011-0366-3",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Poisson point process on the space of lines in R^d, where a multiplicative factor u>0 of the intensity measure determines the density of lines. Each line in the process is taken as the axis of a bi-infinite cylinder of radius 1. We investigate percolative properties of the vacant set, defined as the subset of R^d that is not covered by any such cylinder. We show that in dimensions d >= 4, there is a critical value u_*(d) \\in (0,\\infty), such that with probability 1, the vacant set has an unbounded component if u<u_*(d), and only bounded components if u>u_*(d). For d=3, we prove that the vacant set does not percolate for large u and that the vacant set intersected with a two-dimensional subspace of R^d does not even percolate for small u>0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-10T11:52:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "82B26",
      "60K35"
    ],
    "keywords": [
      "vacant set",
      "poisson cylinders",
      "percolation",
      "poisson point process",
      "intensity measure determines"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5338T"
    }
  }
}