{
  "titles": [
    {
      "title": "On the variational method for Euclidean quantum fields in infinite volume"
    }
  ],
  "creators": [
    {
      "name": "Barashkov, Nikolay",
      "nameType": "Personal",
      "familyName": "Barashkov",
      "givenName": "Nikolay"
    },
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2021,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/2112.05562v2",
  "dates": [
    {
      "date": "2021-12-09",
      "dateType": "Issued"
    },
    {
      "date": "2022-11-21",
      "dateType": "Available"
    },
    {
      "date": "2026-11-14",
      "dateType": "Updated"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-texmacs",
    "application/x-bibtex"
  ],
  "subjects": [
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math-ph",
      "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 investigate the infinite volume limit of the variational description of Euclidean quantum fields introduced in a previous work. Focussing on two dimensional theories for simplicity, we prove in details how to use the variational approach to obtain tightness of $\\varphi^4_2$ without cutoffs and a corresponding large deviation principle for any infinite volume limit. Any infinite volume measure is described via a forward–backwards stochastic differential equation in weak form (wFBSDE). Similar considerations apply to more general $P (\\varphi)_2$ theories. We consider also the $\\exp (\\beta \\varphi)_2$ model for $\\beta^2 < 8 \\pi$ (the so called full $L^1$ regime) and prove uniqueness of the infinite volume limit and a variational characterization of the unique infinite volume measure. The corresponding characterization for $P (\\varphi)_2$ theories is lacking due to the difficulty of studying the stability of the wFBSDE against local perturbations.",
      "descriptionType": "Abstract"
    },
    {
      "description": "Journal reference: Prob. Math. Phys. 4 (2023) 761-801",
      "descriptionType": "SeriesInformation"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:2112.05562v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.2112.05562",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    },
    {
      "relatedIdentifier": "10.2140/pmp.2023.4.761",
      "relatedIdentifierType": "DOI",
      "relationType": "IsPreprintOf"
    }
  ]
}