{
  "abstract": "We compute the fourth-order correction to the full-collision asymptotics of the correlation functions of the $\\mathrm{Sine}_β$ process. For $m \\ge 2$ and $mβ> 3$, the normalized correlation has an expansion through order $ε^4$, with an explicit rational coefficient depending on the centered profile only through its fourth power sum and the square of its second power sum. The remainder is $o(ε^4)$, locally uniformly in the collision profile. We evaluate the required fourth inverse moments of the Hua-Pickrell environment by finite-dimensional Ward identities and prove their convergence using characteristic-polynomial derivative bounds. A fourth-order expectation-Taylor lemma handles the full range $mβ> 3$ without requiring fourth moments of every analytic derivative. For general unitary ensembles with a $C^4$ confining potential and a regular bulk point, we prove convergence of the finite-particle fusion coefficients through fourth order and a joint second-order limit, using complex kernel universality and divided differences. This unitary result imposes no fused-environment hypotheses. For arbitrary $β$, we retain a conditional quadratic transfer criterion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11543",
  "author_total": 1,
  "authors": [
    {
      "name": "Weiyang Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qmn7e0sjhk6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11543",
  "fulltext_url": null,
  "id": "4qmn7e0sjhk6g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11543",
  "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",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7212301478",
  "pdf_url": "https://arxiv.org/pdf/2609.11543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4qmn7e0sjhk6g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fourth-Order Fusion Asymptotics for $\\mathrm{Sine}_β$ Correlation Functions",
  "title_text": "Fourth-Order Fusion Asymptotics for Sine_β Correlation Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/4qmn7e0sjhk6g",
  "venue": "arXiv",
  "versions": []
}