{
  "id": "1905.00379",
  "version": "v1",
  "published": "2019-05-01T16:59:04.000Z",
  "updated": "2019-05-01T16:59:04.000Z",
  "title": "Local metrics of the Gaussian free field",
  "authors": [
    "Ewain Gwynne",
    "Jason Miller"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce the concept of a local metric of a Gaussian free field (GFF) $h$, which is a random metric coupled with $h$ in such a way that it depends locally on $h$ in a certain sense. This definition is a metric analog of the concept of a local set for $h$. We establish general criteria for two local metrics of the same GFF $h$ to be bi-Lipschitz equivalent to each other and for a local metric to be a.s. determined by $h$. Our results are used in subsequent works which prove the existence, uniqueness, and basic properties of the $\\gamma$-Liouville quantum gravity (LQG) metric for all $\\gamma \\in (0,2)$, but no knowledge of LQG is needed to understand this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-01T16:59:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian free field",
      "local metric",
      "liouville quantum gravity",
      "random metric",
      "metric analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}