{
  "abstract": "We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of $O_λ(m)$ for the monomer-dimer model at activity $λ$ and $O_{b,λ}(m)$ for $b$-matchings at fugacity $λ>0$, where $m$ is the number of edges. For uniform $b$-matchings, the relaxation-time bound improves to $O(bm)$. The main proof ideas were found using GPT-5.6 Sol.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18835",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaoyu Chen"
    },
    {
      "name": "Zejia Chen"
    },
    {
      "name": "Xinyuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0z19hhnaxv67q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18835",
  "fulltext_url": null,
  "id": "0z19hhnaxv67q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18835",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213499490",
  "pdf_url": "https://arxiv.org/pdf/2609.18835",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0z19hhnaxv67q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18835",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18835"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Degree-Free Spectral Independence for Log-Concave Holant Measures",
  "title_text": "Degree-Free Spectral Independence for Log-Concave Holant Measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/0z19hhnaxv67q",
  "venue": "arXiv",
  "versions": []
}