{
  "abstract": "We establish the large-$n$ asymptotics of Hankel determinants for unitary random matrix ensembles possessing a higher-order edge singularity. We focus on ensembles where the equilibrium measure is supported on a single interval and the limiting eigenvalue density vanishes to order $2k+\\frac{1}{2}$ for $k \\in \\mathbb{N}$. Notably, we explicitly evaluate the constant term in the asymptotic expansion, which involves a regularized integral of the Hamiltonian associated with the Painlevé I ($P_{\\rm I}^{2k}$) hierarchy. As a by-product, we also prove the universality of the eigenvalue correlation kernel near this singular edge and derive a limiting kernel expressed through functions related to a special solution of the $P_{\\rm I}^{2k}$ equation. Our method relies on the Deift-Zhou nonlinear steepest descent analysis for the Riemann-Hilbert problem of orthogonal polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26412",
  "author_total": 3,
  "authors": [
    {
      "name": "Dan Dai"
    },
    {
      "name": "Jia-Hao Du"
    },
    {
      "name": "Chenhao Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xcv2kff49zg3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26412",
  "fulltext_url": null,
  "id": "0xcv2kff49zg3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26412",
  "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.MP"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214069316",
  "pdf_url": "https://arxiv.org/pdf/2609.26412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xcv2kff49zg3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.26412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Asymptotics of Hankel determinants for potentials with singular edge points",
  "title_text": "Asymptotics of Hankel determinants for potentials with singular edge points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/0xcv2kff49zg3",
  "venue": "arXiv",
  "versions": []
}