{
  "id": "1312.1324",
  "version": "v2",
  "published": "2013-12-04T20:49:53.000Z",
  "updated": "2014-02-06T15:44:45.000Z",
  "title": "KPZ relation does not hold for the level lines and the SLE$_κ$ flow lines of the Gaussian free field",
  "authors": [
    "Juhan Aru"
  ],
  "comment": "47 pages; 4 beautiful images and 2 other figures; in ver2: extended SLE winding theorem 5.1 to also cover the case \\kappa = 4; minor revisions all over the paper",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution and the KPZ relation in a natural way, shedding new light on all of them. Our principal result shows that the level lines and the SLE$_\\kappa$ flow lines of the Gaussian free field do not satisfy the usual KPZ relation. In order to prove this, we have to make a technical detour: by a careful study of a certain diffusion process, we provide exact estimates of the exponential moments of winding of chordal SLE curves conditioned to pass nearby a fixed point. This extends previous results on winding of SLE curves by Schramm.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-06T15:44:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian free field",
      "level lines",
      "flow lines",
      "usual kpz relation",
      "chordal sle curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1267896,
      "adsabs": "2013arXiv1312.1324A"
    }
  }
}