{
  "abstract": "We study a Brownian particle in $\\mathbb{R}^d$, $d\\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The proof uses a renormalization group induction: at each scale, the elliptic operator is well approximated by a Laplacian with effective diffusivity decaying as a power of scale. We compute this exponent exactly in dimension two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12335",
  "author_total": 3,
  "authors": [
    {
      "name": "Scott Armstrong"
    },
    {
      "name": "Ahmed Bou-Rabee"
    },
    {
      "name": "Tuomo Kuusi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8424pm286088p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12335",
  "fulltext_url": null,
  "id": "8424pm286088p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12335",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7221143859",
  "pdf_url": "https://arxiv.org/pdf/2610.12335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8424pm286088p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Anomalous scaling limit of a Brownian particle in a log-correlated potential",
  "title_text": "Anomalous scaling limit of a Brownian particle in a log-correlated potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/8424pm286088p",
  "venue": "arXiv",
  "versions": []
}