{
  "abstract": "We consider the adjacency matrix of a uniformly random simple $d$-regular graph on $N$ vertices. For every fixed $d\\geq3$ and every fixed bulk energy, we prove that the rescaled eigenvalue point process converges to the $\\mathrm{Sine}_1$ process with intensity $1/π$. We also establish universality of consecutive gaps at deterministic bulk labels and of fixed-energy correlation measures. The eigenvector input consists of polynomial estimates for mixed fourth moments on a uniformly sampled star. These estimates prevent loss of variance in the qualitative joint Gaussian limits of Backhausz--Szegedy, yielding independent variance-one Gaussian waves for fixed tuples at nearby energies. Exact switching identities then give a stationary marked flow and the microscopic loop hierarchy, which identifies the point-process limit. The appendices prove the stronger correlation and gap statements using counting-moment bounds and conditional log-gas laws for tagged limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08127",
  "author_total": 3,
  "authors": [
    {
      "name": "Yukun He"
    },
    {
      "name": "Jiaoyang Huang"
    },
    {
      "name": "Xiaoyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/920hg9jw5yeq8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08127",
  "fulltext_url": null,
  "id": "920hg9jw5yeq8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08127",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7220978146",
  "pdf_url": "https://arxiv.org/pdf/2610.08127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/920hg9jw5yeq8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.08127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08127"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Bulk universality of random regular graphs",
  "title_text": "Bulk universality of random regular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/920hg9jw5yeq8",
  "venue": "arXiv",
  "versions": []
}