{
  "abstract": "For tempered Langevin diffusions (TLDs) targeting polynomially tailed measures, the convergence rate is known to change from polynomial to exponential to uniform as the temperature rises through a critical value. We explain this transition by the tails of the marginal laws of the norm of the TLD, up to a second, larger critical temperature beyond which the TLD explodes. As the temperature increases, these tails change from stretched-exponential, through super-polynomial at the first critical temperature, to polynomial, mirroring the transition in the convergence rate. Moreover, this tail analysis gives a complete quantification of the convergence rates throughout the non-explosive regime, in both $f$-variation and Wasserstein distances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30024",
  "author_total": 2,
  "authors": [
    {
      "name": "Aleksandar Mijatović"
    },
    {
      "name": "Haokai Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3984xsnh8vbfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30024",
  "fulltext_url": null,
  "id": "3984xsnh8vbfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30024",
  "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"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7223212781",
  "pdf_url": "https://arxiv.org/pdf/2610.30024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3984xsnh8vbfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.30024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Tempered Langevin diffusions with polynomial-tailed targets: explosions, moment thresholds and ergodicity",
  "title_text": "Tempered Langevin diffusions with polynomial-tailed targets: explosions, moment thresholds and ergodicity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/3984xsnh8vbfa",
  "venue": "arXiv",
  "versions": []
}