{
  "titles": [
    {
      "title": "The FBSDE approach to sine-Gordon up to $6\\pi$"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    },
    {
      "name": "Meyer, Sarah-Jean",
      "nameType": "Personal",
      "familyName": "Meyer",
      "givenName": "Sarah-Jean"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2024,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "3",
  "url": "https://arxiv.org/abs/2401.13648v3",
  "dates": [
    {
      "date": "2024-01-24",
      "dateType": "Issued"
    },
    {
      "date": "2026-06-17",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math-ph",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.MP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "Creative Commons Attribution 4.0 International",
      "rightsIdentifier": "cc-by-4.0",
      "rightsUri": "http://creativecommons.org/licenses/by/4.0/",
      "rightsIdentifierScheme": "SPDX"
    }
  ],
  "descriptions": [
    {
      "description": "We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\\cos (\\beta \\varphi))_2$ on the full space up to the second threshold, i.e. for $\\beta^2 < 6 \\pi$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition $(X_t)_{t \\geqslant 0}$ of the interacting Euclidean field $X_{\\infty}$ along a scale parameter $t \\geqslant 0$. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the interacting field without cut-offs and that it can be used effectively to study the sine-Gordon measure to obtain results about large deviations, integrability, decay of correlations for local observables, singularity with respect to the free field, Osterwalder-Schrader axioms and other properties.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:2401.13648v3",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.2401.13648",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}