{
  "id": "1410.3715",
  "version": "v1",
  "published": "2014-10-14T14:48:29.000Z",
  "updated": "2014-10-14T14:48:29.000Z",
  "title": "Conformal invariance of crossing probabilities for the Ising model with free boundary conditions",
  "authors": [
    "Stéphane Benoist",
    "Hugo Duminil-Copin",
    "Clément Hongler"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin. We do so by establishing the convergence of certain exploration processes towards SLE$(3,\\frac{-3}2,\\frac{-3}2)$. We also construct an exploration tree for free boundary conditions, analogous to the one introduced by Sheffield.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-14T14:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J67",
      "82B20"
    ],
    "keywords": [
      "free boundary conditions",
      "crossing probabilities",
      "conformal invariance",
      "critical planar ising model",
      "phenomenon first"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.3715B"
    }
  }
}