{
  "id": "1305.5444",
  "version": "v2",
  "published": "2013-05-23T15:02:31.000Z",
  "updated": "2015-08-17T18:29:20.000Z",
  "title": "The time of bootstrap percolation in two dimensions",
  "authors": [
    "Paul Balister",
    "Béla Bollobás",
    "Paul Smith"
  ],
  "comment": "39 pages, 6 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study the distribution of the percolation time $T$ of two-neighbour bootstrap percolation on $[n]^2$ with initial set $A\\sim\\mathrm{Bin}([n]^2,p)$. We determine $T$ with high probability up to a constant factor for all $p$ above the critical probability for percolation, and to within a $1+o(1)$ factor for a large range of $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-23T15:02:31.000Z",
      "abstract": "We study the distribution of the percolation time $T$ of two-neighbour bootstrap percolation on $[n]^2$ with initial set $A\\sim\\bin([n]^2,p)$. We determine $T$ with high probability up to a constant factor for all $p$ above the critical probability for percolation, and to within a $1+o(1)$ factor for a large range of $p$.",
      "comment": "36 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-17T18:29:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensions",
      "two-neighbour bootstrap percolation",
      "percolation time",
      "constant factor",
      "initial set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5444B"
    }
  }
}