{
  "abstract": "We study lazy single-site Metropolis dynamics $P_β$ at inverse temperature $β\\geq 0$ on $\\{-1,+1\\}^d$ for an Ising star with additional signed interactions among the leaves. If the absolute row sums of the leaf-interaction matrix are at most $κ\\le1/2$, the worst-case total-variation mixing time of $P_β$ is at least of order $d\\exp\\{cβ(d-1)\\}$ for $β\\ge1$, with universal $c>0$. Averaging over global spin reversal reduces the mixing time to $\\mathcal O(d^2(1+β))$ for both $GP_βG$ and $(P_β+G)/2$, where $G$ is the Gibbs kernel induced by the partition of the state space into spin-reversal orbits $\\{-x,x\\}$. Partition-function interpolation gives the lower bound for $P_β$. The upper bounds follow from Wu's Dobrushin inequality and a decomposition into projection and restriction chains. This gives an explicit example in which group averaging turns an exponentially slow chain into a polynomially fast one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15023",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael C. H. Choi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3v4veg5s1zxj0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15023",
  "fulltext_url": null,
  "id": "3v4veg5s1zxj0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15023",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7213354442",
  "pdf_url": "https://arxiv.org/pdf/2609.15023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3v4veg5s1zxj0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "From torpid to rapid mixing: group averaging for a weakly interacting Ising star",
  "title_text": "From torpid to rapid mixing: group averaging for a weakly interacting Ising star",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/3v4veg5s1zxj0",
  "venue": "arXiv",
  "versions": []
}