{
  "id": "1106.0200",
  "version": "v2",
  "published": "2011-06-01T15:07:33.000Z",
  "updated": "2011-06-14T08:47:37.000Z",
  "title": "Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane",
  "authors": [
    "Christoph Thaele"
  ],
  "journal": "Braz. J. Probab. Stat. 28, 73-82 (2014)",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Poisson Boolean model. The Hausdorff-dimension of the set of directions is determined in terms of the $\\alpha$-value of Z in which visibility from a fixed point to the ideal boundary of the hyperbolic plane is possible within Z. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in Z is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm and Tykesson are confirmed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-14T08:47:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "28A80",
      "60D05",
      "28A78",
      "82C21",
      "82B43"
    ],
    "keywords": [
      "hyperbolic plane",
      "well-behaved continuum percolation",
      "visibility sets",
      "hausdorff dimension",
      "poisson boolean model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0200T"
    }
  }
}