{
  "abstract": "It is proved that, for every $δ\\in (0,1)$, the Glauber dynamics for the uniform distribution on proper $q$-colorings is rapidly mixing when $q \\geq (1+δ)Δ$ and the underlying graph has girth at least $5$ and maximum degree $Δ= Ω_δ(1)$. This result also extends to general multi-spin systems satisfying a $\\textit{local spectral contraction}$ condition, including the anti-ferromagnetic Potts model with $q\\geq (1+δ)(1-β)Δ$. These results are achieved by a new spectral local-to-global principle on graphs with girth at least five for general multi-spin systems, and a novel Fourier analysis for Glauber dynamics on a star. The main ideas behind all the proofs were developed through several rounds of interaction with GPT-5.6 Sol Ultra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25491",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaoyu Chen"
    },
    {
      "name": "Kuikui Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6j2adsnj1jky2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25491",
  "fulltext_url": null,
  "id": "6j2adsnj1jky2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25491",
  "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"
    ],
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      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7204461376",
  "pdf_url": "https://arxiv.org/pdf/2608.25491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6j2adsnj1jky2.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2608.25491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Spectral Local-to-Global Principle for Spin Systems on Graphs with Girth At Least Five",
  "title_text": "A Spectral Local-to-Global Principle for Spin Systems on Graphs with Girth At Least Five",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/6j2adsnj1jky2",
  "venue": "arXiv",
  "versions": []
}