{
  "id": "1803.00354",
  "version": "v1",
  "published": "2018-03-01T13:21:56.000Z",
  "updated": "2018-03-01T13:21:56.000Z",
  "title": "Poisson cylinders in hyperbolic space",
  "authors": [
    "Erik I. Broman",
    "Johan H. Tykesson"
  ],
  "comment": "29 pages",
  "journal": "Electronic Journal of Probability, Vol. 20 (2015), Paper 41",
  "doi": "10.1214/EJP.v20-3645",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Poisson cylinder model in $d$-dimensional hyperbolic space. We show that in contrast to the Euclidean case, there is a phase transition in the connectivity of the collection of cylinders as the intensity parameter varies. We also show that for any non-trivial intensity, the diameter of the collection of cylinders is infinite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-01T13:21:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "poisson cylinder model",
      "dimensional hyperbolic space",
      "intensity parameter varies",
      "phase transition",
      "collection"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}