{
  "id": "math/0412510",
  "version": "v2",
  "published": "2004-12-28T11:28:01.000Z",
  "updated": "2005-10-04T22:20:51.000Z",
  "title": "Sharp thresholds and percolation in the plane",
  "authors": [
    "Bela Bollobas",
    "Oliver Riordan"
  ],
  "comment": "28 pages, 8 figures. Minor revisions and additions. To appear in Random Structures and Algorithms",
  "journal": "Random Structures and Algorithms 29 (2006), 524--548.",
  "doi": "10.1002/rsa.20134",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square lattice. The aim of this paper is to show that the same techniques can be applied to many other planar percolation models, both to obtain short proofs of known results, and to prove new ones.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-04T22:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "sharp thresholds",
      "harris-kesten theorem concerning bond percolation",
      "short proof",
      "random voronoi percolation",
      "planar square lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12510B"
    }
  }
}