{
  "abstract": "We determine the first correction to the leading Vandermonde fusion law for the correlation functions of the Sine$*β$ process in the critical and and subcritical regimes $mβ\\leq1$. When $mβ<1$, the normalized correction is of order $|\\varepsilon|^{1+mβ}$, with a strictly negative coefficient given by an explicit gamma-function ratio times an absolutely convergent arithmetic-geometric mean deficit integral. At $mβ=1$, it is $-\\frac{\\sum*{i<j}(a_i-a_j)^2}{8m^2(2m+1)}\\varepsilon^2\\log(1/|\\varepsilon|)+O(\\varepsilon^2)$. For two merging points, the subcritical coefficient reduces to a gamma-function expression involving $\\sec(πβ)-1$, and the critical logarithmic coefficient is $-1/160$. The argument starts from a geometric interpolation of circular-Jacobi weights. Selecting one particle in the interpolation derivative increases the fused charge by $β$ and leaves a strict positive-power moment margin in the remaining stochastic-zeta expectation. This yields an absolutely convergent one-particle identity and uniform control at the collision scale. The results resolve the critical and subcritical conjecture in the author's earlier preprint and complement its supercritical second-order expansion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07239",
  "author_total": 1,
  "authors": [
    {
      "name": "Weiyang Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vsj2v0h0cx0f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07239",
  "fulltext_url": null,
  "id": "8vsj2v0h0cx0f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07239",
  "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": "W7212032891",
  "pdf_url": "https://arxiv.org/pdf/2609.07239",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vsj2v0h0cx0f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07239",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07239"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Critical and subcritical fusion asymptotics for Sine$_β$ correlation functions",
  "title_text": "Critical and subcritical fusion asymptotics for Sine_β correlation functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8vsj2v0h0cx0f",
  "venue": "arXiv",
  "versions": []
}