{
  "abstract": "We present an open-source Python package for sampling the Gaussian, Laguerre, Jacobi, and Circular $β$-ensembles of random matrix theory. The package implements the Dumitriu--Edelman and Killip--Nenciu constructions, allowing efficient generation of random spectra for general $β> 0$. In addition to spectrum generation, it includes tools for the analysis of spectral statistics, from standard nearest-neighbor spacings and spacing ratios to non-adjacent $k$-spacings and the spectral form factor. These tools can be applied to generic spectral data, allowing users to compare them with and fit them to $β$-ensemble predictions. In this note, we review the $β$-ensembles, describe the package interface, and illustrate its use through several numerical experiments motivated by applications to quantum chaos. Our numerical results include an analysis of $β$ as a continuous fitting parameter in spacing ratio statistics, an examination of the numerical evidence for the conjectured $k$-spacing ratio distributions, and a study of the spectral form factor for general values of $β$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27224",
  "author_total": 1,
  "authors": [
    {
      "name": "Dorin Weissman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/da2tthvtxnbk8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27224",
  "fulltext_url": null,
  "id": "da2tthvtxnbk8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27224",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7204561712",
  "pdf_url": "https://arxiv.org/pdf/2608.27224",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/da2tthvtxnbk8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2608.27224",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27224"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics",
  "title_text": "Exploring continuous beta-ensembles: A Python implementation for random matrix spectral statistics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/da2tthvtxnbk8",
  "venue": "arXiv",
  "versions": []
}