{
  "id": "2409.10037",
  "version": "v1",
  "published": "2024-09-16T06:58:25.000Z",
  "updated": "2024-09-16T06:58:25.000Z",
  "title": "Singularity of solutions to singular SPDEs",
  "authors": [
    "Martin Hairer",
    "Seiichiro Kusuoka",
    "Hirotatsu Nagoji"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Building on the notes [Hai17], we give a sufficient condition for the marginal distribution of the solution of singular SPDEs on the $d$-dimensional torus to be singular with respect to the law of the Gaussian measure induced by the linearised equation. As applications we obtain the singularity of the $\\Phi^4_3$-measure with respect to the Gaussian free field measure and the border of parameters for the fractional $\\Phi^4$-measure to be singular with respect to the Gaussian free field measure. Our approach is applicable to quite a large class of singular SPDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-16T06:58:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H17"
    ],
    "keywords": [
      "singular spdes",
      "gaussian free field measure",
      "singularity",
      "dimensional torus",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}