{
  "abstract": "Consider the circular beta-ensembles, Jiang and Matsumoto computed the moments of traces, and proved central limit theorems for polynomial linear statistics using Jack functions. We give a direct proof of the Gaussian limits for the traces of powers of circular beta-ensembles using the theory of orthogonal polynomials on the unit circle and Stein's method. The proof relies on an explicit coupling of the Verblunsky coefficients of circular beta-ensembles, which also allow us to obtain almost sure and $L^2$ convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01803",
  "author_total": 1,
  "authors": [
    {
      "name": "Yun Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7p27avf6z2ezk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01803",
  "fulltext_url": null,
  "id": "7p27avf6z2ezk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01803",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7216014394",
  "pdf_url": "https://arxiv.org/pdf/2610.01803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7p27avf6z2ezk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Gaussian limits for traces of circular beta-ensembles",
  "title_text": "Gaussian limits for traces of circular beta-ensembles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/7p27avf6z2ezk",
  "venue": "arXiv",
  "versions": []
}