{
  "abstract": "We consider the long-time behavior of a diffusion process on $\\mathbb{R}^{d} $ R d advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case includes $\\nabla ^{\\perp }$ ∇ ⊥ of the Gaussian free field in two dimensions. We show the variance and the second moment of the displacement at a large time $t$ t behave like $2dc_{*}^{\\nicefrac 12} t (\\log t)^{\\nicefrac 12}$ , in a quenched sense and with a precisely determined prefactor $c_{*}= c_{*}( \\mathbb{P} )>0$ c ∗ = c ∗ ( P ) > 0 , independent of $\\nu $ ν . We also prove a quenched invariance principle under this superdiffusive scaling. The proof is based on a rigorous renormalization group argument in which we inductively analyze coarse-grained diffusivities, scale-by-scale. Our analysis leads to sharp homogenization and large-scale regularity estimates on the infinitesimal generator, which are subsequently transferred into quantitative information on the process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Scott N. Armstrong",
      "orcid": "0000-0002-1395-081X"
    },
    {
      "name": "Ahmed Bou‐Rabee",
      "orcid": "0000-0002-8794-2847"
    },
    {
      "name": "Tuomo Kuusi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dt96r6jw982sx.bib",
  "cited_by": 44,
  "doi": "10.1007/s00222-026-01455-z",
  "fulltext_url": null,
  "id": "dt96r6jw982sx",
  "issns": [
    "0020-9910",
    "1432-1297"
  ],
  "landing_url": "https://doi.org/10.1007/s00222-026-01455-z",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W4393741148",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00222-026-01455-z.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/dt96r6jw982sx.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W4393741148",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00222-026-01455-z"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift",
  "title_text": "Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/dt96r6jw982sx",
  "venue": "Inventiones mathematicae",
  "versions": []
}