{
  "abstract": "Determining exact joint eigenvalue densities is central to random matrix theory. We solve this long-standing problem for non-Hermitian matrices with transposition symmetry (complex symmetric and complex self-dual) at arbitrary matrix size. Up to a Vandermonde factor, they are scattering-state wave functions of the Calogero model, a line of particles interacting through an inverse-square potential, with the coupling strength set by the symmetry. In contrast to many previously known joint densities, the densities cannot be written as a gas of eigenvalues with pairwise interactions. We further compute the complex level spacing distributions and two-point spectral correlation functions, which carry power-law tails, absent in a Coulomb gas. Our results shed light on the interplay among random matrices, integrability, and symmetry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00164",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhenyu Xiao"
    },
    {
      "name": "Ze Chen"
    },
    {
      "name": "Shinsei Ryu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4x61azeezxs68.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00164",
  "fulltext_url": null,
  "id": "4x61azeezxs68",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00164",
  "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.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7206161337",
  "pdf_url": "https://arxiv.org/pdf/2609.00164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4x61azeezxs68.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.00164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00164"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exact joint eigenvalue densities of non-Hermitian random matrices are Calogero scattering states",
  "title_text": "Exact joint eigenvalue densities of non-Hermitian random matrices are Calogero scattering states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/4x61azeezxs68",
  "venue": "arXiv",
  "versions": []
}