{
  "id": "1301.1165",
  "version": "v1",
  "published": "2013-01-07T12:05:54.000Z",
  "updated": "2013-01-07T12:05:54.000Z",
  "title": "Zebra-percolation on Cayley trees",
  "authors": [
    "D. Gandolfo",
    "U. A. Rozikov",
    "J. Ruiz"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider Bernoulli (bond) percolation with parameter $p$ on the Cayley tree of order $k$. We introduce the notion of zebra-percolation that is percolation by paths of alternating open and closed edges. In contrast with standard percolation with critical threshold at $p_c= 1/k$, we show that zebra-percolation occurs between two critical values $p_{{\\rm c},1}$ and $p_{{\\rm c},2}$ (explicitly given). We provide the specific formula of zebra-percolation function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-07T12:05:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "cayley tree",
      "standard percolation",
      "zebra-percolation occurs",
      "specific formula",
      "zebra-percolation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1165G"
    }
  }
}