{
  "id": "math/9811170",
  "version": "v2",
  "published": "1998-11-29T07:08:43.000Z",
  "updated": "1999-05-02T06:14:33.000Z",
  "title": "Indistinguishability of Percolation Clusters",
  "authors": [
    "Russell Lyons",
    "Oded Schramm"
  ],
  "comment": "To appear in Ann. Probab",
  "journal": "AnnalsProbab.27:1809-1836,1999",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that when percolation produces infinitely many infinite clusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property. This implies that uniqueness of the infinite cluster is equivalent to non-decay of connectivity (a.k.a. long-range order). We then derive applications concerning uniqueness in Kazhdan groups and in wreath products, and inequalities for $p_u$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-05-02T06:14:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "60B99",
      "60K35",
      "60D05"
    ],
    "keywords": [
      "percolation clusters",
      "indistinguishability",
      "infinite cluster",
      "cayley graph",
      "long-range order"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1214/aop/1022677549"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 492588,
      "adsabs": "1998math.....11170L"
    }
  }
}