{
  "id": "2110.03656",
  "version": "v1",
  "published": "2021-10-07T17:45:30.000Z",
  "updated": "2021-10-07T17:45:30.000Z",
  "title": "Boundary renormalisation of SPDEs",
  "authors": [
    "Máté Gerencsér",
    "Martin Hairer"
  ],
  "comment": "51 pages",
  "journal": "Comm. PDE, Vol 47, 2070-2123 (2022)",
  "doi": "10.1080/03605302.2022.2109173",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider the continuum parabolic Anderson model (PAM) and the dynamical $\\Phi^4$ equation on the $3$-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for $\\Phi^4_3$ a `boundary triviality' result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-10-07T17:45:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60L30"
    ],
    "keywords": [
      "continuum parabolic anderson model",
      "dirichlet boundary conditions",
      "divergent boundary renormalisation",
      "neumann/robin boundary conditions",
      "usual bulk renormalisation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}