{
  "id": "1105.2638",
  "version": "v2",
  "published": "2011-05-13T07:56:38.000Z",
  "updated": "2012-07-28T15:34:30.000Z",
  "title": "Uniqueness of percolation on products with Z",
  "authors": [
    "Itai Benjamini",
    "Gady Kozma"
  ],
  "comment": "10 pages. New version includes one result in the positive direction",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that there exists a connected graph G with subexponential volume growth such that critical percolation on the product of G with the line has infinitely many infinite clusters. We also give some conditions under which this cannot occur.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-28T15:34:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "uniqueness",
      "subexponential volume growth",
      "infinite clusters",
      "critical percolation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.2638B"
    }
  }
}