{
  "id": "math/0604487",
  "version": "v2",
  "published": "2006-04-22T15:03:55.000Z",
  "updated": "2006-11-07T11:04:45.000Z",
  "title": "Critical Percolation Exploration Path and SLE(6): a Proof of Convergence",
  "authors": [
    "Federico Camia",
    "Charles M. Newman"
  ],
  "comment": "45 pages, 14 figures; revised version following the comments of a referee",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE(6). We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE(6) that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-07T11:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B27",
      "60K35",
      "82B43",
      "60D05",
      "30C35"
    ],
    "keywords": [
      "critical percolation exploration path",
      "convergence",
      "critical site percolation exploration path",
      "critical percolation full scaling limit",
      "triangular lattice converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4487C"
    }
  }
}