{
  "id": "0904.3965",
  "version": "v2",
  "published": "2009-04-25T07:10:06.000Z",
  "updated": "2009-07-25T09:27:28.000Z",
  "title": "Metastable behavior for bootstrap percolation on regular trees",
  "authors": [
    "Marek Biskup",
    "Roberto H. Schonmann"
  ],
  "comment": "10 pages, version to appear in J. Statist. Phys",
  "journal": "J. Statist. Phys. 136 (2009), no. 4, 667-676",
  "doi": "10.1007/s10955-009-9798-x",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least theta occupied neighbors, occupied sites remain occupied forever. It is known that, when b>theta>1, the limiting density q=q(p) of occupied sites exhibits a jump at some p_t=p_t(b,theta) in (0,1) from q_t:=q(p_t)<1 to q(p)=1 when p>p_t. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p_t+h with h>0 and show that, as h decreases to 0, the system lingers around the \"critical\" state for time order h^{-1/2} and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q in (q_t,1) converges, as h tends to 0, to a well-defined measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-25T09:27:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C43",
      "82C22",
      "82C05"
    ],
    "keywords": [
      "bootstrap percolation",
      "metastable behavior",
      "regular trees",
      "occupied sites remain occupied forever",
      "vacant site"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2009,
      "month": "Aug",
      "volume": 136,
      "number": 4,
      "pages": 667
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JSP...136..667B"
    }
  }
}