{
  "id": "math/0509131",
  "version": "v2",
  "published": "2005-09-06T18:58:30.000Z",
  "updated": "2005-09-10T19:42:03.000Z",
  "title": "A note on the Harris-Kesten Theorem",
  "authors": [
    "Bela Bollobas",
    "Oliver Riordan"
  ],
  "comment": "4 pages; author list changed, acknowledgement added",
  "journal": "Europ. J. Combin. 28 (2007), 1720-1723.",
  "doi": "10.1016/j.ejc.2006.05.022",
  "categories": [
    "math.PR"
  ],
  "abstract": "Recently, a short proof of the Harris-Kesten result that the critical probability for bond percolation in the planar square lattice is 1/2 was given, using a sharp threshold result of Friedgut and Kalai. Here we point out that a key part of this proof may be replaced by an argument of Russo from 1982, using his approximate zero-one law in place of the Friedgut-Kalai result. Russo's paper gave a new proof of the Harris-Kesten Theorem that seems to have received little attention.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-10T19:42:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "harris-kesten theorem",
      "approximate zero-one law",
      "sharp threshold result",
      "russos paper gave",
      "planar square lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9131B"
    }
  }
}