{
  "id": "math/0209343",
  "version": "v2",
  "published": "2002-09-25T16:17:37.000Z",
  "updated": "2003-04-25T21:11:07.000Z",
  "title": "Conformal restriction: the chordal case",
  "authors": [
    "Gregory Lawler",
    "Oded Schramm",
    "Wendelin Werner"
  ],
  "comment": "To appear in JAMS",
  "journal": "J.Am.Math.Soc.16:917-955,2003",
  "doi": "10.1090/S0894-0347-03-00430-2",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "We characterize and describe all random subsets $K$ of a given simply connected planar domain (the upper half-plane $\\H$, say) which satisfy the ``conformal restriction'' property, i.e., $K$ connects two fixed boundary points (0 and $\\infty$, say) and the law of $K$ conditioned to remain in a simply connected open subset $D$ of $\\H$ is identical to that of $\\Phi(K)$, where $\\Phi$ is a conformal map from $\\H$ onto $D$ with $\\Phi(0)=0$ and $\\Phi(\\infty)=\\infty$. The construction of this family relies on the stochastic Loewner evolution (SLE) processes with parameter $\\kappa \\le 8/3$ and on their distortion under conformal maps. We show in particular that SLE(8/3) is the only random simple curve satisfying conformal restriction and relate it to the outer boundaries of planar Brownian motion and SLE(6).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-04-25T21:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60J65",
      "30C99"
    ],
    "keywords": [
      "chordal case",
      "simple curve satisfying conformal restriction",
      "random simple curve satisfying conformal",
      "conformal map",
      "planar brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 610521,
      "adsabs": "2002math......9343L"
    }
  }
}