{
  "id": "1107.0158",
  "version": "v3",
  "published": "2011-07-01T09:19:15.000Z",
  "updated": "2013-06-07T08:55:17.000Z",
  "title": "Planar percolation with a glimpse of Schramm-Loewner Evolution",
  "authors": [
    "Vincent Beffara",
    "Hugo Duminil-Copin"
  ],
  "comment": "Survey based on lectures given in \"La Pietra week in Probability\", Florence, Italy, 2011. (2013)",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "In recent years, important progress has been made in the field of two-dimensional statistical physics. One of the most striking achievements is the proof of the Cardy-Smirnov formula. This theorem, together with the introduction of Schramm-Loewner Evolution and techniques developed over the years in percolation, allow precise descriptions of the critical and near-critical regimes of the model. This survey aims to describe the different steps leading to the proof that the infinite-cluster density $\\theta(p)$ for site percolation on the triangular lattice behaves like $(p-p_c)^{5/36+o(1)}$ as $p\\searrow p_c=1/2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-07T08:55:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schramm-loewner evolution",
      "planar percolation",
      "triangular lattice behaves",
      "important progress",
      "precise descriptions"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0158B"
    }
  }
}