{
  "id": "math/0604261",
  "version": "v1",
  "published": "2006-04-11T21:06:01.000Z",
  "updated": "2006-04-11T21:06:01.000Z",
  "title": "On the connectivity of the Poisson process on fractals",
  "authors": [
    "Gady Kozma",
    "Zvi Lotker",
    "Gideon Stupp"
  ],
  "comment": "5 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a measure mu supported on a compact connected subset of a Euclidean space which satisfies a uniform d-dimensional decay of the volume of balls we show that the maximal edge in the minimum spanning tree of n indepndent samples from mu is, with high probability (log n/n)^(1/d).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-11T21:06:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "60D05",
      "60K35"
    ],
    "keywords": [
      "poisson process",
      "connectivity",
      "uniform d-dimensional decay",
      "compact connected subset",
      "euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4261K"
    }
  }
}