{
  "abstract": "We study correlators of the Jacobi Unitary Ensemble $\\mathbf J(p,q,α,β,N)$ of Hermitian matrices with spectrum in an arbitrary real interval $[p,q]$. For $(p,q)=(0,1)$, Gisonni, Grava and Ruzza expressed the large-$N$ expansion of the correlators $\\langle\\prod_j \\mathrm{tr}\\,X^{λ_j}\\rangle$ through triple monotone Hurwitz numbers. We extend this genus expansion to arbitrary $p,q$ with $α/N$ and $β/N$ fixed. Using the Frobenius characteristic map and the idempotent basis of the center of $\\mathbb C[\\mathfrak S_n]$, we also obtain an explicit formula for the Schur--Selberg type integral $\\int_{(p,q)^N}χ_λ(x)\\,Δ^2(x)\\prod_a (q-x_a)^β(x_a-p)^α\\,\\mathrm{d}^Nx$ in terms of irreducible characters of the symmetric group and content products. As consequences, we describe the zero-mean ensemble, and we recover, term by term in the genus expansion, the polygon-gluing formula for the Gaussian Unitary Ensemble in the limit $c_A=c_B\\to\\infty$. Structurally, passing from $[0,1]$ to $[p,q]$ leaves the hypergeometric weight of the associated 2D Toda tau function unchanged and only changes the specialization of its second set of times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02795",
  "author_total": 1,
  "authors": [
    {
      "name": "Matvey Sushkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5h0brhb03qy3a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02795",
  "fulltext_url": null,
  "id": "5h0brhb03qy3a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02795",
  "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.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "arxiv",
      "nlin.SI"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02795",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5h0brhb03qy3a.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02795",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02795"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Correlators of the Jacobi Unitary Ensemble on a General Interval and Hurwitz Numbers",
  "title_text": "Correlators of the Jacobi Unitary Ensemble on a General Interval and Hurwitz Numbers",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5h0brhb03qy3a",
  "venue": "arXiv",
  "versions": []
}