{
  "id": "1201.6373",
  "version": "v1",
  "published": "2012-01-30T21:11:24.000Z",
  "updated": "2012-01-30T21:11:24.000Z",
  "title": "Stochastic Domination and Comb Percolation",
  "authors": [
    "Alexander E. Holroyd",
    "James Martin"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of Z^{d-1} joined by a perpendicular copy) into the open set of site percolation on Z^d, whenever the parameter p is close enough to 1 or the Lipschitz constant is sufficiently large. This is proved using several new results and techniques involving stochastic domination, in contexts that include a process of independent overlapping intervals on Z, and first-passage percolation on general graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-30T21:11:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "stochastic domination",
      "comb percolation",
      "d-dimensional comb graph",
      "first-passage percolation",
      "general graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.6373H"
    }
  }
}