{
  "id": "2102.07032",
  "version": "v1",
  "published": "2021-02-13T23:33:21.000Z",
  "updated": "2021-02-13T23:33:21.000Z",
  "title": "Large deviations of Schramm-Loewner evolutions: A survey",
  "authors": [
    "Yilin Wang"
  ],
  "comment": "41 pages, 3 figures",
  "categories": [
    "math.PR",
    "math.CV"
  ],
  "abstract": "These notes survey the first and recent results on large deviations of Schramm-Loewner evolutions (SLE) with the emphasis on interrelations among rate functions and applications to complex analysis. More precisely, we describe the large deviations of SLE$_\\kappa$ when the $\\kappa$ parameter goes to zero in the chordal and multichordal case and to infinity in the radial case. The rate functions, namely Loewner and Loewner-Kufarev energies, are closely related to the Weil-Petersson class of quasicircles and real rational functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-13T23:33:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations",
      "schramm-loewner evolutions",
      "rate functions",
      "real rational functions",
      "weil-petersson class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}