{
  "abstract": "We consider the adjacency matrix of a random directed $d$-regular graph on $N$ vertices. For fixed $d\\geq 2$, we prove that the empirical eigenvalue density converges in probability to the oriented Kesten--McKay law as $N\\to \\infty$. The key technical input is the small-ball probability estimate for the smallest singular value. The proof combines a fixed-rank transposition argument with finite-field anticoncentration for shifted inverse compressions. We also prove a polynomial hard-edge estimate, which allows us to deduce the global law from the vanishing small-ball probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05297",
  "author_total": 2,
  "authors": [
    {
      "name": "Yukun He"
    },
    {
      "name": "Jiaoyang Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xwwjjfzacexz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05297",
  "fulltext_url": null,
  "id": "2xwwjjfzacexz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05297",
  "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": "W7211884794",
  "pdf_url": "https://arxiv.org/pdf/2609.05297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xwwjjfzacexz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The oriented Kesten--McKay law for random regular digraphs",
  "title_text": "The oriented Kesten--McKay law for random regular digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/2xwwjjfzacexz",
  "venue": "arXiv",
  "versions": []
}