{
  "id": "math/0405074",
  "version": "v1",
  "published": "2004-05-05T13:11:01.000Z",
  "updated": "2004-05-05T13:11:01.000Z",
  "title": "Excursion decompositions for $\\SLE$ and Watts' crossing formula",
  "authors": [
    "Julien Dubedat"
  ],
  "comment": "36 pages",
  "journal": "Probab. Theory Related Fields 134 (2006), no. 3, 453--488",
  "doi": "10.1007/s00440-005-0446-3",
  "categories": [
    "math.PR"
  ],
  "abstract": "It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if $\\kappa>4$ and a.s. cutpoints if $4<\\kappa<8$. If $\\kappa>4$, an appropriate version of $\\SLE(\\kappa)$ has a renewal property: it starts afresh after visiting its frontier. Thus one can give an excursion decomposition for this particular $\\SLE(\\kappa)$ ``away from its frontier''. For $4<\\kappa<8$, there is a two-sided analogue of this situation: a particular version of $\\SLE(\\kappa)$ has a renewal property w.r.t its cutpoints; one studies excursion decompositions of this $\\SLE$ ``away from its cutpoints''. For $\\kappa=6$, this overlaps Vir\\'ag's results on ``Brownian beads''. As a by-product of this construction, one proves Watts' formula, which describes the probability of a double crossing in a rectangle for critical plane percolation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-05T13:11:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43",
      "60G18",
      "60G51"
    ],
    "keywords": [
      "crossing formula",
      "renewal property",
      "studies excursion decompositions",
      "overlaps virags results",
      "schramm-loewner evolutions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5074D"
    }
  }
}