{
  "abstract": "In this paper, we study the random polynomial $p_n(\\rho):=\\prod_{j=1}^n (|z_j|-\\rho)$, where the points $\\{z_j\\}_{j=1}^n$ are the eigenvalues of random normal matrices with a radially symmetric potential. We establish precise large $n$ asymptotic expansions for the moment generating function $\\mathbb{E}\\bigl[{\\rm e}^{(u \\operatorname{Im}\\log p_n(\\rho))/\\pi} {\\rm e}^{a\\operatorname{Re}\\log p_n(\\rho)}\\bigr]$, $u\\in\\mathbb{R}$, $a>-1$, where $\\rho>0$ lies in the bulk of the spectral droplet. The asymptotic expansion is expressed in terms of parabolic cylinder functions, which confirms a conjecture of Byun and Charlier. This also provides the first free energy expansion of two-dimensional Coulomb gases with general circular root- and jump-type singularities. While the $a=0$ case has already been widely studied in the literature due to its relation to counting statistics, we also obtain new results for this special case.",
  "abstract_shown": true,
  "affiliations": [
    "Université Catholique de Louvain, Belgium"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Kohei Noda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yxn1vwph1j00.bib",
  "cited_by": 0,
  "doi": "10.3842/sigma.2026.106",
  "fulltext_url": null,
  "id": "0yxn1vwph1j00",
  "issns": [
    "1815-0659"
  ],
  "landing_url": "https://sigma-journal.com/2026/106/",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "SIGMA (Symmetry, Integrability and Geometry: Methods and Application)",
  "ris": "https://research.draconitic.com/paper/0yxn1vwph1j00.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T00:20:45Z",
      "native_id": "10.3842/sigma.2026.106",
      "source": "crossref",
      "url": "https://sigma-journal.com/2026/106/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1815-0659",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Partition Functions of Two-Dimensional Coulomb Gases with Circular Root- and Jump-Type Singularities",
  "title_text": "Partition Functions of Two-Dimensional Coulomb Gases with Circular Root- and Jump-Type Singularities",
  "type": "peer-reviewed",
  "updated_at": "2026-11-01T00:20:43Z",
  "url": "https://research.draconitic.com/paper/0yxn1vwph1j00",
  "venue": "Symmetry, Integrability and Geometry: Methods and Applications",
  "versions": []
}