{
  "id": "1101.1527",
  "version": "v2",
  "published": "2011-01-07T21:08:58.000Z",
  "updated": "2011-07-18T05:00:38.000Z",
  "title": "Geometry of the random interlacement",
  "authors": [
    "Eviatar B. Procaccia",
    "Johan Tykesson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in \\cite{benjamini2004geometry} to prove the following: Given that two vertices $x,y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $\\lceil d/2 \\rceil$ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $\\lceil d/2 \\rceil-1$ trajectories.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-18T05:00:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random interlacement",
      "interlacement set",
      "underlying poisson point process",
      "stochastic dimension theory",
      "dimensional lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1527P"
    }
  }
}