{
  "id": "math/0308112",
  "version": "v1",
  "published": "2003-08-12T11:41:50.000Z",
  "updated": "2003-08-12T11:41:50.000Z",
  "title": "A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models",
  "authors": [
    "Federico Camia",
    "Charles M. Newman",
    "Vladas Sidoravicius"
  ],
  "comment": "25 pages, 7 figures",
  "doi": "10.1007/s00220-004-1042-6",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study families of dependent site percolation models on the triangular lattice ${\\mathbb T}$ and hexagonal lattice ${\\mathbb H}$ that arise by applying certain cellular automata to independent percolation configurations. We analyze the scaling limit of such models and show that the distance between macroscopic portions of cluster boundaries of any two percolation models within one of our families goes to zero almost surely in the scaling limit. It follows that each of these cellular automaton generated dependent percolation models has the same scaling limit (in the sense of Aizenman-Burchard [3]) as independent site percolation on ${\\mathbb T}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-08-12T11:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B27",
      "60K35",
      "82B43",
      "82C20",
      "82C43",
      "37B15",
      "68Q80"
    ],
    "keywords": [
      "scaling limit",
      "automaton generated dependent percolation models",
      "cellular automaton generated dependent percolation",
      "dependent site percolation models",
      "universality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2004,
      "volume": 246,
      "number": 2,
      "pages": 311
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004CMaPh.246..311C"
    }
  }
}