{
  "id": "2401.07695",
  "version": "v1",
  "published": "2024-01-15T14:09:29.000Z",
  "updated": "2024-01-15T14:09:29.000Z",
  "title": "Gaussian multiplicative chaos on a ball",
  "authors": [
    "Anna Talarczyk-Noble",
    "Maciej Wiśniewolski"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide representations of the Laplace transforms of GMC on Euclidean balls $B(0,r)$, $r\\in (0,1]$. Up to non-vanishing spatial mean, the small deviations of Gaussian multiplicative chaos $M$ associated to the Lebesgue measure on ball are of log-normal type $$ \\ln\\Big(\\mathbb{E}e^{-e^tM}\\Big) = -c t^2 + o(t^2), \\quad t\\rightarrow \\infty. $$ We find the bounds on optimal constants $c = c(r)$ associated to small deviations of GMC on balls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T14:09:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G60"
    ],
    "keywords": [
      "gaussian multiplicative chaos",
      "small deviations",
      "euclidean balls",
      "optimal constants",
      "laplace transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}