{
  "abstract": "We determine the joint moments of real powers of the absolute value of characteristic polynomials in the circular beta ensemble, for every $β>0$. At fixed distinct prescribed points, the Fisher--Hartwig formula holds for every exponent greater than $-1$, with explicit constants and a relative error bounded by a negative power of the matrix size $N$. For approaching points in the same integrable range, the error is bounded by a negative power of $Nδ_N$, provided that $Nδ_N\\to\\infty$ and the sum of the absolute values of the negative exponents is less than two. Here $δ_N$ is the minimum distance between the prescribed points; this range includes every integrable pair of root exponents. For $q>0$ at the critical relation $pq^2=2β$, we prove the Keating--Wong asymptotic for the $p$th moment of the integral of the $q$th absolute power of the characteristic polynomial, for every real $p>1$. The leading asymptotic extends to every complex spatial weight in $L^p$. The proofs combine the recursion for orthogonal polynomials on the unit circle with conditional expectation identities for Gaussian multiplicative chaos and quantitative estimates for approaching singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02205",
  "author_total": 4,
  "authors": [
    {
      "name": "Reda Chhaibi"
    },
    {
      "name": "Pierre-Loïc Méliot"
    },
    {
      "name": "Joseph Najnudel"
    },
    {
      "name": "Ashkan Nikeghbali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0w0jerancq7kh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02205",
  "fulltext_url": null,
  "id": "0w0jerancq7kh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02205",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02205",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0w0jerancq7kh.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02205",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02205"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fisher--Hartwig asymptotics and critical moments for the circular beta ensemble",
  "title_text": "Fisher--Hartwig asymptotics and critical moments for the circular beta ensemble",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/0w0jerancq7kh",
  "venue": "arXiv",
  "versions": []
}