{
  "abstract": "We study the LOVÁSZ number of dense random circulant graphs generated by independent Bernoulli bits indexed by cyclic distances. Although only $O(n)$ independent random inputs determine $O(n^2)$ globally dependent edge indicators, we prove sharp expectation asymptotics along all odd orders, including composite orders, with leading constant one. This resolves a conjecture posed for random circulant graphs in 2025. The proof combines an exact Fourier reduction and complementary duality with a positive interior smoothing that reveals a nonlinear random fixed-point equation. To analyze this equation under the strong dependence of the distance-bit model, we construct canonical tree fields, establish growing-degree Gaussian approximations through polynomial comparison and Wick/Hermite expansions, and transfer the resulting approximation back to the original sign model. A deterministic residual estimate together with an explicit exceptional-event integration yields the sharp expectation asymptotics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22971",
  "author_total": 5,
  "authors": [
    {
      "name": "Xin Chen"
    },
    {
      "name": "Hongwei Hu"
    },
    {
      "name": "Yanqing Hu"
    },
    {
      "name": "Wei Wang"
    },
    {
      "name": "Luzhen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30k9kj8wn6kbg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22971",
  "fulltext_url": null,
  "id": "30k9kj8wn6kbg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22971",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7222947378",
  "pdf_url": "https://arxiv.org/pdf/2610.22971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30k9kj8wn6kbg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sharp asymptotics for the Lovász number of random circulant graphs",
  "title_text": "Sharp asymptotics for the Lovász number of random circulant graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/30k9kj8wn6kbg",
  "venue": "arXiv",
  "versions": []
}