{
  "abstract": "We consider a Coulomb gas on a Jordan curve $γ$ in an external potential $V$ at inverse temperature $β>0$ and obtain an asymptotic expansion of the free energy up to $o(1)$ and a central limit theorem for linear statistics. We focus on the one-cut regime, where the density of the weighted equilibrium measure of $γ$ in $V$ is strictly positive on $γ$. The constant term in the (normalized) expansion consists of two parts: the Fredholm determinant of a generalized Grunsky operator and the Dirichlet energy of the logarithm of the density of the weighted equilibrium measure of $γ$. The coefficient of the latter vanishes for $β=2$. The variance of the fluctuations of the linear statistics only depends on the Dirichlet energy of the test function and is therefore independent of $V$. Essential in our approach is that the generalized Grunsky operator and the accompanying equilibrium parametrization allow us to transport the particles on the curve in the external potential to a reference object in a way that preserves the equilibrium measure. In our setting, the unit circle is the natural reference object.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20675",
  "author_total": 2,
  "authors": [
    {
      "name": "Kurt Johansson"
    },
    {
      "name": "Thomas Wolfs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cw80mrhe70wqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20675",
  "fulltext_url": null,
  "id": "cw80mrhe70wqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20675",
  "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",
      "math.CV"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7213587573",
  "pdf_url": "https://arxiv.org/pdf/2609.20675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cw80mrhe70wqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Limit theorems for Coulomb gases on a Jordan curve in an external potential",
  "title_text": "Limit theorems for Coulomb gases on a Jordan curve in an external potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/cw80mrhe70wqr",
  "venue": "arXiv",
  "versions": []
}