{
  "abstract": "We study fixed-temperature logarithmic and Riesz gases after subtracting the leading mean-field contribution relative to a prescribed background law. For repulsive interactions in the Hilbert--Schmidt regime, we prove $N$-uniform bounds and quantitative convergence of the resulting modulated partition function to a normalization expressed by the Carleman--Fredholm determinant of the centered interaction operator. We show that the Hilbert--Schmidt threshold is sharp and obtain explicit lower bounds on the rate of divergence at and above it; these rates are expected to be nonoptimal. The proof combines positive-definite truncations and a low/high-frequency decomposition with exponential inequalities and Gaussian-chaos asymptotics for canonical degree-two $U$-statistics. As consequences, we establish entropic commutator estimates with the sharp $O(N^{-1})$ additive scale in the modulated-free-energy method, a static joint linear-statistics central limit theorem, and a dynamical central limit theorem for joint linear statistics at finitely many times. This extends the logarithmic partition-function estimates of the first two authors to the full Riesz Hilbert--Schmidt range and identifies the limiting determinant normalization. For the attractive logarithmic interaction at sufficiently small inverse temperature, we also prove analogous results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02743",
  "author_total": 3,
  "authors": [
    {
      "name": "Matias G. Delgadino"
    },
    {
      "name": "Rishabh Gvalani"
    },
    {
      "name": "Matthew Rosenzweig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/enr5svj855rzt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02743",
  "fulltext_url": null,
  "id": "enr5svj855rzt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02743",
  "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"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
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  "openalex": "W7207605345",
  "pdf_url": "https://arxiv.org/pdf/2609.02743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/enr5svj855rzt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02743"
    }
  ],
  "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": "Sharp mean-field estimates for diffusive log/Riesz gases in the Hilbert--Schmidt regime",
  "title_text": "Sharp mean-field estimates for diffusive log/Riesz gases in the Hilbert--Schmidt regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/enr5svj855rzt",
  "venue": "arXiv",
  "versions": []
}