{
  "id": "1509.05015",
  "version": "v1",
  "published": "2015-09-16T19:40:04.000Z",
  "updated": "2015-09-16T19:40:04.000Z",
  "title": "Decomposition of Schramm-Loewner evolution along its curve",
  "authors": [
    "Dapeng Zhan"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that, for $\\kappa\\in(0,8)$, the integral of the laws of two-sided radial SLE$_\\kappa$ curves through different interior points against a measure with SLE$_\\kappa$ Green function density is the law of a chordal SLE$_\\kappa$ curve, biased by the path's natural length. We also show that, for $\\kappa>0$, the integral of the laws of extended SLE$_\\kappa(-8)$ curves through different interior points against a measure with a closed formula density restricted in a bounded set is the law of a chordal SLE$_\\kappa$ curve, biased by the path's capacity length restricted in that set. Another result is that, for $\\kappa\\in(4,8)$, if one integrates the laws of two-sided chordal SLE$_\\kappa$ curves through different force points on $\\mathbb R$ against a measure with density on $\\mathbb R$, then one also gets a law that is absolutely continuous w.r.t. that of a chordal SLE$_\\kappa$ curve. To obtain these results, we develop a framework to study stochastic processes with random lifetime, and improve the traditional Girsanov's Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-16T19:40:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schramm-loewner evolution",
      "chordal sle",
      "decomposition",
      "interior points",
      "green function density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905015Z"
    }
  }
}