{
  "abstract": "Sampling from high-dimensional, heavy-tailed distributions is a fundamental challenge in computational statistics, as many standard Markov chain Monte Carlo (MCMC) methods mix poorly in such settings. Recently, Stereographic MCMC [Yang et al., 2024] and the Sub-Cauchy Projection Sampler [Grazzi et al., 2026] have been shown to perform successfully on such tasks. However, establishing their non-asymptotic convergence properties remains an important open problem. In this work, we fill this gap by establishing non-asymptotic upper bounds on the mixing time of the stereographic projection and sub-Cauchy projection samplers. Our results demonstrate that, under certain conditions on the target and initial distributions, the mixing time is polynomial in dimension for a broad class of distributions, including light- and heavy-tailed cases. Motivated by the theoretical analysis, we further establish a new weighted isoperimetric inequality that extends the classical version for log-concave distributions to the heavy-tailed setting with optimal dimension dependence. The proof techniques provide new insights into the geometric properties of heavy-tailed distributions that govern rapid mixing in high dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18513",
  "author_total": 3,
  "authors": [
    {
      "name": "Federica Milinanni"
    },
    {
      "name": "Tyler Farghly"
    },
    {
      "name": "Jun Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6dmt670wbt8q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18513",
  "fulltext_url": null,
  "id": "f6dmt670wbt8q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18513",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221765418",
  "pdf_url": "https://arxiv.org/pdf/2610.18513",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6dmt670wbt8q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18513",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18513"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling",
  "title_text": "Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/f6dmt670wbt8q",
  "venue": "arXiv",
  "versions": []
}