{
  "id": "math/0410359",
  "version": "v3",
  "published": "2004-10-15T21:41:05.000Z",
  "updated": "2005-06-16T15:14:58.000Z",
  "title": "A short proof of the Harris-Kesten Theorem",
  "authors": [
    "Bela Bollobas",
    "Oliver Riordan"
  ],
  "comment": "17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical Society",
  "journal": "Bulletin of the London Mathematical Society 38 (2006), 470--484.",
  "doi": "10.1112/S002460930601842X",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any $p>1/2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-16T15:14:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "short proof",
      "harris-kesten theorem",
      "planar square lattice",
      "bond percolation",
      "fundamental result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10359B"
    }
  }
}