{
  "id": "1507.00218",
  "version": "v1",
  "published": "2015-07-01T13:11:08.000Z",
  "updated": "2015-07-01T13:11:08.000Z",
  "title": "Remarks on the intersection of SLE$_κ(ρ)$ curve with the real line",
  "authors": [
    "Menglu Wang",
    "Hao Wu"
  ],
  "comment": "All comment are welcome",
  "categories": [
    "math.PR"
  ],
  "abstract": "SLE$_{\\kappa}(\\rho)$ is a variant of SLE$_{\\kappa}$ where $\\rho$ characterizes the repulsion (if $\\rho>0$) or attraction $(\\rho<0)$ from the boundary. This paper examines the probabilities of SLE$_{\\kappa}(\\rho)$ to get close to the boundary. We show how close the chordal SLE$_{\\kappa}(\\rho)$ curves get to the boundary asymptotically, and provide an estimate for the probability that the SLE$_{\\kappa}(\\rho)$ curve hits graph of functions. These generalize the similar result derived by Schramm and Zhou for standard SLE$_{\\kappa}$ curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-01T13:11:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "28A80"
    ],
    "keywords": [
      "real line",
      "intersection",
      "curve hits graph",
      "standard sle",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150700218W"
    }
  }
}