{
  "id": "1412.3839",
  "version": "v1",
  "published": "2014-12-11T22:07:13.000Z",
  "updated": "2014-12-11T22:07:13.000Z",
  "title": "Level Lines of Gaussian Free Field I: Zero-Boundary GFF",
  "authors": [
    "Menglu Wang",
    "Hao Wu"
  ],
  "comment": "77 pages, 43 figures. All comments are welcome",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $h$ be an instance of Gaussian Free Field in a planar domain. We study level lines of $h$ starting from boundary points. We show that the level lines are random continuous curves which are variants of SLE$_4$ path. We show that the level lines with different heights satisfy the same monotonicity behavior as the level lines of smooth functions. We prove that the time-reversal of the level line coincides with the level line of $-h$. This implies that the time-reversal of SLE$_4(\\underline{\\rho})$ process is still an SLE$_4(\\underline{\\rho})$ process. We prove that the level lines satisfy \"target-independent\" property. We also discuss the relation between Gaussian Free Field and CLE$_4$ which is a collection of SLE$_4$-loops.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-11T22:07:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian free field",
      "zero-boundary gff",
      "study level lines",
      "level line coincides",
      "level lines satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3839W"
    }
  }
}