{
  "titles": [
    {
      "title": "Global solutions to elliptic and parabolic $\\Phi^4$ models in Euclidean space"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    },
    {
      "name": "Hofmanová, Martina",
      "nameType": "Personal",
      "familyName": "Hofmanová",
      "givenName": "Martina"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2018,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/1804.11253v2",
  "dates": [
    {
      "date": "2018-04-30",
      "dateType": "Issued"
    },
    {
      "date": "2019-01-25",
      "dateType": "Available"
    },
    {
      "date": "2026-11-14",
      "dateType": "Updated"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math-ph",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.AP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.MP",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors",
      "rightsUri": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
    }
  ],
  "descriptions": [
    {
      "description": "We prove existence of global solutions to singular SPDEs on $\\mathbb{R}^d$ with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions $d=4,5$ and in the parabolic setting for $d=2,3$. We prove uniqueness and coming down from infinity for the parabolic equations. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the $\\Phi^4_d$ Euclidean quantum field theory via Parisi–Wu stochastic quantization, while the elliptic equations are linked to the $\\Phi^4_{d-2}$ Euclidean quantum field theory via the Parisi–Sourlas dimensional reduction mechanism.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:1804.11253v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.1804.11253",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    },
    {
      "relatedIdentifier": "10.1007/s00220-019-03398-4",
      "relatedIdentifierType": "DOI",
      "relationType": "IsPreprintOf"
    }
  ]
}