{
  "id": "1406.0491",
  "version": "v4",
  "published": "2014-06-02T19:42:50.000Z",
  "updated": "2018-06-19T16:17:43.000Z",
  "title": "Liouville heat kernel: regularity and bounds",
  "authors": [
    "Pascal Maillard",
    "Rémi Rhodes",
    "Vincent Vargas",
    "Ofer Zeitouni"
  ],
  "comment": "49 pages. Journal version",
  "journal": "Ann. Inst. H. Poincar\\'e Probab. Statist., 52(3), 1281-1320, 2016",
  "doi": "10.1214/15-AIHP676",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We initiate in this paper the study of analytic properties of the Liouville heat kernel. In particular, we establish regularity estimates on the heat kernel and derive non trivial lower and upper bounds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-12T15:45:31.000Z",
      "comment": "49 pages. New version includes lower bound for all gamma, when points are sampled according to M_gamma",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2018-06-19T16:17:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K08",
      "60J60",
      "60K37",
      "60J55",
      "60J70"
    ],
    "keywords": [
      "liouville heat kernel",
      "derive non trivial lower",
      "analytic properties",
      "upper bounds",
      "establish regularity estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1298929,
      "adsabs": "2014arXiv1406.0491M"
    }
  }
}