{
  "id": "1305.0154",
  "version": "v1",
  "published": "2013-05-01T12:17:59.000Z",
  "updated": "2013-05-01T12:17:59.000Z",
  "title": "Spectral dimension of Liouville quantum gravity",
  "authors": [
    "Rémi Rhodes",
    "Vincent Vargas"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper is concerned with computing the spectral dimension of 2d-Liouville quantum gravity. As a warm-up, we first treat the simple case of boundary Liouville quantum gravity. We prove that the spectral dimension is 1 via an exact expression for the boundary Liouville Brownian motion and heat kernel. Then we treat the 2d-case via a decomposition of time integral transforms of the Liouville heat kernel into Gaussian multiplicative chaos of Brownian bridges. We show that the spectral dimension is 2 in this case, as announced by physicists (see Ambj\\orn and al. in \\cite{amb}) fifteen years ago.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-01T12:17:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral dimension",
      "boundary liouville brownian motion",
      "boundary liouville quantum gravity",
      "liouville heat kernel",
      "time integral transforms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00023-013-0308-y"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1231664,
      "adsabs": "2014AnHP...15.2281R"
    }
  }
}