{
  "abstract": "The Bingham distribution is widely used to model directional data with antipodal symmetry, and its normalizing constant $Z$ and moments play a central role in statistical inference and closure models. Their behavior becomes singular when one or more eigenvalue gaps of the parameter matrix become unbounded. In this work, we develop a uniform asymptotic framework for the Bingham distribution in arbitrary dimensions. Starting from an inverse-Laplace integral representation, we derive asymptotic expansions with explicit remainder estimates that are uniform with respect to arbitrary relative scales among multiple diverging eigenvalues. In a particular regime, the asymptotic series becomes absolutely convergent with an exponentially small remainder. These results yield precise asymptotic profiles of the Bingham moments and characterize the degeneration of higher-dimensional distributions to lower-dimensional counterparts. As an application to the Bingham closure, we prove that the entropy admits a decomposition into an explicit logarithmic leading term and a residual that is uniformly Lipschitz continuous on the moment simplex. Moreover, on each boundary face, the residual agrees with its lower-dimensional version up to an explicit additive constant. The results provide a unified description of the singular structure of the Bingham distribution and have implications for numerical closure and $Q$-tensor models of nematic liquid crystals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07121",
  "author_total": 3,
  "authors": [
    {
      "name": "Dawei Wu"
    },
    {
      "name": "Lei Zhang"
    },
    {
      "name": "Pingwen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qagcjcgc5jt0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07121",
  "fulltext_url": null,
  "id": "3qagcjcgc5jt0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07121",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7212022781",
  "pdf_url": "https://arxiv.org/pdf/2609.07121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qagcjcgc5jt0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.07121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Uniform asymptotics and entropy structure of the Bingham distribution in arbitrary dimensions",
  "title_text": "Uniform asymptotics and entropy structure of the Bingham distribution in arbitrary dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3qagcjcgc5jt0",
  "venue": "arXiv",
  "versions": []
}