{
  "id": "1304.6357",
  "version": "v1",
  "published": "2013-04-23T17:30:44.000Z",
  "updated": "2013-04-23T17:30:44.000Z",
  "title": "Connectedness of Poisson cylinders in Euclidean space",
  "authors": [
    "Erik I. Broman",
    "Johan Tykesson"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Poisson cylinder model in ${\\mathbb R}^d$, $d\\ge 3$. We show that given any two cylinders ${\\mathfrak c}_1$ and ${\\mathfrak c}_2$ in the process, there is a sequence of at most $d-2$ other cylinders creating a connection between ${\\mathfrak c}_1$ and ${\\mathfrak c}_2$. In particular, this shows that the union of the cylinders is a connected set, answering a question appearing in a previous paper. We also show that there are cylinders in the process that are not connected by a sequence of at most $d-3$ other cylinders. Thus, the diameter of the cluster of cylinders equals $d-2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-23T17:30:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60D05"
    ],
    "keywords": [
      "euclidean space",
      "connectedness",
      "poisson cylinder model",
      "cylinders equals",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.6357B"
    }
  }
}