{
  "id": "1410.5407",
  "version": "v1",
  "published": "2014-10-20T19:47:41.000Z",
  "updated": "2014-10-20T19:47:41.000Z",
  "title": "Liouville quantum gravity and the Gaussian free field",
  "authors": [
    "Nathanaël Berestycki",
    "Scott Sheffield",
    "Xin Sun"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given an instance $h$ of the Gaussian free field on a planar domain $D$ and a constant $\\gamma \\in (0,2)$, one can use various regularization procedures to make sense of the {\\em Liouville quantum gravity measure} $$\\mu_h := e^{\\gamma h(z)} dz.$$ It is known that the field $h$ a.s. determines the measure $\\mu_h$. We show that the converse is true: namely, given $\\mu_h$, it is a.s. possible to recover $h$. We then use this result to show that the path of a Liouville Brownian motion also determines the free field $h$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-20T19:47:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian free field",
      "liouville quantum gravity measure",
      "liouville brownian motion",
      "regularization procedures",
      "determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1322998,
      "adsabs": "2014arXiv1410.5407B"
    }
  }
}