{
  "id": "0909.4499",
  "version": "v1",
  "published": "2009-09-24T17:01:32.000Z",
  "updated": "2009-09-24T17:01:32.000Z",
  "title": "Critical percolation in the plane",
  "authors": [
    "Stanislav Smirnov"
  ],
  "comment": "This is a copy of an old preprint from 2001, which I will perhaps update in the future",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy's formula. Then we prove existence, uniqueness, and conformal invariance of the continuum scaling limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-24T17:01:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "30C35",
      "81T40",
      "82B43"
    ],
    "keywords": [
      "critical percolation",
      "conformal invariance",
      "harmonic conformal invariants",
      "cardys formula",
      "critical site percolation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4499S"
    }
  }
}