{
  "abstract": "A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness threshold. Their approach builds upon the literature of various local-to-global techniques and applies to a more general setting of discrete distributions supported on downward-closed set families. We give a short and self-contained proof via a Bochner--Bakry--Émery approach and directly show a Poincaré inequality by expanding the Dirichlet form in terms of the $L^2$-norm of the generator applied to a test function and eliminating a sum of squares term. Our proof is a streamlined version of an argument of Kondratiev, Kuna, and Ohlerich used to study spatial birth-and-death dynamics for Gibbs point processes in the continuum, which we adapt to the discrete setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "name": "Andreas Göbel",
      "orcid": "0000-0002-5180-7205"
    },
    {
      "name": "Matthew Jenssen",
      "orcid": "0000-0003-0026-8501"
    },
    {
      "name": "Marcus Michelen"
    },
    {
      "name": "Marcus Pappik",
      "orcid": "0000-0002-2480-3073"
    },
    {
      "name": "Will Perkins",
      "orcid": "0000-0002-7937-7016"
    },
    {
      "name": "Leon Schiller",
      "orcid": "0000-0001-7315-237X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fsx4edf0dd0z.bib",
  "cited_by": 13,
  "doi": "10.48550/arxiv.2606.27545",
  "fulltext_url": null,
  "id": "4fsx4edf0dd0z",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2606.27545",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
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  "openalex": "W7166562581",
  "pdf_url": "https://arxiv.org/pdf/2606.27545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-25",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/4fsx4edf0dd0z.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T13:20:57Z",
      "native_id": "W7166562581",
      "source": "openalex",
      "url": "https://arxiv.org/abs/2606.27545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A simple proof of rapid mixing on random regular graphs beyond uniqueness",
  "title_text": "A simple proof of rapid mixing on random regular graphs beyond uniqueness",
  "type": "preprint",
  "updated_at": "2026-11-10T13:20:57Z",
  "url": "https://research.draconitic.com/paper/4fsx4edf0dd0z",
  "venue": "arXiv (Cornell University)",
  "versions": []
}