{
  "abstract": "We show that for every $γ>0$ and every sufficiently large $Δ$, the Glauber dynamics for proper $q$-colorings of any $n$-vertex graph of maximum degree $Δ$ has spectral gap $Ω_γ(1/n)$, and hence mixing time $O_γ(n^2\\log q)$, whenever $q\\ge(1+1/\\mathrm{e}+γ)Δ$. Our proof establishes a Bochner-type inequality by exploiting the spectral gaps of hard-core models hidden in the color classes. The constant $1+1/\\mathrm{e}\\approx1.368$ comes from the uniqueness threshold $\\approx\\mathrm{e}/Δ$ of the hard-core model on the infinite $Δ$-regular tree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04699",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiongxin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q4ya8sv3sb6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04699",
  "fulltext_url": null,
  "id": "2q4ya8sv3sb6g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04699",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04699",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q4ya8sv3sb6g.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04699",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04699"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Glauber Dynamics for Sampling Colorings: Rapid Mixing above $(1+1/\\mathrm{e})Δ$ via Hidden Hard-Core Models",
  "title_text": "Glauber Dynamics for Sampling Colorings: Rapid Mixing above (1+1/e)Δ via Hidden Hard-Core Models",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/2q4ya8sv3sb6g",
  "venue": "arXiv",
  "versions": []
}