{
  "abstract": "We study the large-scale behaviour of a class of driven diffusive systems modelled by a Stochastic Partial Differential Equation, the Stochastic Burgers Equation (SBE) with general nonlinearity, at the critical dimension and in infinite volume. Our main result shows that, under a logarithmically superdiffusive space-time scaling, it is given by the same explicit Gaussian Fixed point obtained in [G. Cannizzaro, Q. Moulard, & F. Toninelli, https://arxiv.org/abs/2501.00344, 2025] for the quadratic SBE, but with suitably renormalised coefficients, thereby rigorously justifying and partly correcting the classical Physics derivation of the SBE in [H. van Beijeren, R. Kutner, & H. Spohn, Phys. Rev. Lett., 1986] based on Spohn’s theory of nonlinear fluctuating hydrodynamics. Besides, ours is the first universality-type result for out-of-equilibrium systems and the first extension of [M. Hairer, J. Quastel, Forum of Mathematics, Pi, Vol. 6, 2018, e3], to the critical dimension and beyond weak coupling. The major challenge in our work is the mild growth condition on the nonlinearity which renders even the well-posedness of the microscopic equation non-trivial. Additional key novelties include the derivation of fine estimates on the non-quadratic part of the generator as well as a new approximation for the resolvent associated to the solution of the quadratic SBE.",
  "abstract_shown": true,
  "affiliations": [
    "University of Warwick, Coventry, UK",
    "University of Oxford, Oxford, UK",
    "Technical University of Vienna, Vienna, Austria"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Giuseppe Cannizzaro"
    },
    {
      "affs": [
        1
      ],
      "name": "Tom Klose"
    },
    {
      "affs": [
        2
      ],
      "name": "Quentin Moulard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y1axv37j3w57.bib",
  "cited_by": 0,
  "doi": "10.1007/s00440-026-01515-8",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13719755/",
  "id": "5y1axv37j3w57",
  "issns": [
    "0178-8051",
    "1432-2064"
  ],
  "landing_url": "https://doi.org/10.1007/s00440-026-01515-8",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Research"
    ],
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7169566239",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00440-026-01515-8.pdf",
  "pmcid": "PMC13719755",
  "pmid": "42964475",
  "published": "2026-07-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y1axv37j3w57.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:23:40Z",
      "native_id": "PMC13719755",
      "source": "pmc",
      "url": "https://doi.org/10.1007/s00440-026-01515-8"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Superdiffusive central limit theorem for a class of driven diffusive systems at the critical dimension",
  "title_text": "Superdiffusive central limit theorem for a class of driven diffusive systems at the critical dimension",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T12:20:46Z",
  "url": "https://research.draconitic.com/paper/5y1axv37j3w57",
  "venue": "Probability Theory and Related Fields",
  "versions": []
}