{
  "id": "1512.06190",
  "version": "v1",
  "published": "2015-12-19T05:04:32.000Z",
  "updated": "2015-12-19T05:04:32.000Z",
  "title": "Two perspectives of the unit area quantum sphere and their equivalence",
  "authors": [
    "Juhan Aru",
    "Yichao Huang",
    "Xin Sun"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Recently David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) provided two different probabilistic perspectives on Liouville quantum gravity on the sphere. In particular, in each of them one may find a definition of the unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-19T05:04:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "81T40",
      "81T20"
    ],
    "keywords": [
      "equivalence",
      "respective unit area quantum spheres",
      "liouville quantum gravity",
      "probabilistic perspectives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206190A"
    }
  }
}