{
  "id": "1202.1684",
  "version": "v1",
  "published": "2012-02-08T13:01:04.000Z",
  "updated": "2012-02-08T13:01:04.000Z",
  "title": "Cylinders' percolation in three dimensions",
  "authors": [
    "Marcelo Hilário",
    "Vladas Sidoravicius",
    "Augusto Teixeira"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the complementary set of a Poissonian ensemble of infinite cylinders in R^3, for which an intensity parameter u > 0 controls the amount of cylinders to be removed from the ambient space. We establish a non-trivial phase transition, for the existence of an unbounded connected component of this set, as u crosses a critical non-degenerate intensity u*. We moreover show that this complementary set percolates in a sufficiently thick slab, in spite of the fact that it does not percolate in any given plane of R^3, regardless of the choice of u.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-08T13:01:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "82B26",
      "60K35"
    ],
    "keywords": [
      "percolation",
      "dimensions",
      "complementary set percolates",
      "non-trivial phase transition",
      "critical non-degenerate intensity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.1684H"
    }
  }
}