{
  "id": "2103.07273",
  "version": "v1",
  "published": "2021-03-12T13:48:33.000Z",
  "updated": "2021-03-12T13:48:33.000Z",
  "title": "A characterisation of the continuum Gaussian free field in $d \\geq 2$ dimensions",
  "authors": [
    "Juhan Aru",
    "Ellen Powell"
  ],
  "comment": "12 pages, 0 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that under certain mild moment and continuity assumptions, the $d$-dimensional Gaussian free field is the only stochastic process in $d\\geq 2$ that is translation invariant, exhibits a certain scaling, and satisfies the usual domain Markov property. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-12T13:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G60",
      "60J65"
    ],
    "keywords": [
      "continuum gaussian free field",
      "characterisation",
      "dimensions",
      "usual domain markov property",
      "dimensional gaussian free field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}