{
  "id": "1307.0703",
  "version": "v3",
  "published": "2013-07-02T13:37:28.000Z",
  "updated": "2014-05-07T12:35:31.000Z",
  "title": "Thick points for a Gaussian Free Field in 4 dimensions",
  "authors": [
    "Alessandra Cipriani",
    "Rajat Subhra Hazra"
  ],
  "comment": "17 pages. Proof on the support of the Liouville Quantum Gravity added",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article is concerned with the study of the fractal dimension of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on $\\R^4$ introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space $H^2(\\R^4)$. We can prove that for $0\\leq a \\leq 4$ the Hausdorff dimension of the set of $a$-high points is $4-a$. We also show that the set of thick points gives full mass to the 4-dimensional Liouville Quantum Gravity measure.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-07T12:35:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian free field",
      "thick points",
      "liouville quantum gravity measure",
      "abstract wiener space",
      "full mass"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0703C"
    }
  }
}