{
  "abstract": "For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $β^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple, has intensity one, and admits a stationary ordered matching to the unit lattice with the same bounds. Each limit satisfies the canonical Gibbs equations for the full-line interaction, with an ordinary symmetric spatial principal value for the exterior potential. The matching implies uniformly bounded interval number variance and a positive limiting second moment of the reciprocal-lattice Fourier average at sufficiently low temperature. The main estimate compares the inverse random Hessian, through deterministic electrical flows, to a transient long-range network.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28503",
  "author_total": 1,
  "authors": [
    {
      "name": "Yan Ru Pei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e08jtemj3krt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28503",
  "fulltext_url": null,
  "id": "e08jtemj3krt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28503",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.PR"
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      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7214359969",
  "pdf_url": "https://arxiv.org/pdf/2609.28503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e08jtemj3krt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28503"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Uniform displacement bounds and Gibbs limits for periodic one-dimensional Riesz gases",
  "title_text": "Uniform displacement bounds and Gibbs limits for periodic one-dimensional Riesz gases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/e08jtemj3krt4",
  "venue": "arXiv",
  "versions": []
}