{
  "abstract": "We study how a functional inequality satisfied by the one-particle conditional distributions of a Gibbs measure, with a constant independent of the positions of the other particles, can be propagated to the whole N -particle system, with a constant independent of N , when the interaction is singular. Our model is the Coulomb gas on the torus T 3 in the mean-field regime. We distinguish two mechanisms. The first one is a dependent tensorization, governed by Dobrushin-Wu interdependence coefficients. It yields uniform Poincar{é} and transport-information W 2 I inequalities with fully explicit constants. We explain why this mechanism does not extend to the log-Sobolev inequality: the Zegarlinski-type coefficients, which require pointwise bounds on the interaction, are infinite. The second mechanism is a tensorization with a defect. Using a uniform bound on the partition function due to Duerinckx and Jabin, it yields a uniform log-Sobolev inequality for the Coulomb gas on T 3 at small charge. We identify the assumptions on the interaction under which each mechanism applies. All the results are then extended to the two-dimensional Coulomb gas and to periodic Riesz gases 1/|x|^s , 0 < s $\\le$ 1. The extension to d $\\ge$ 4 is also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35350",
  "author_total": 4,
  "authors": [
    {
      "name": "A Guillin"
    },
    {
      "name": "W Liu"
    },
    {
      "name": "B Nectoux"
    },
    {
      "name": "L Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zjg7fhf3tttj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35350",
  "fulltext_url": null,
  "id": "8zjg7fhf3tttj",
  "issns": [],
  "landing_url": "https://hal.science/hal-05839088v2",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "0.math"
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      "hal",
      "1.math.math-fa"
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      "1.math.math-mp"
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    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7223814038",
  "pdf_url": "https://hal.science/hal-05839088/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zjg7fhf3tttj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05839088",
      "source": "hal",
      "url": "https://hal.science/hal-05839088v2"
    },
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.35350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "From one particle to N particles: uniform transport-information and log-Sobolev inequalities for Coulomb gases on the torus",
  "title_text": "From one particle to N particles: uniform transport-information and log-Sobolev inequalities for Coulomb gases on the torus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/8zjg7fhf3tttj",
  "venue": "HAL",
  "versions": []
}