{
  "abstract": "We study invariant position distributions in the Smoluchowski-Kramers approximation for Langevin equations driven by rotationally symmetric \\(α\\)-stable noise, with \\(α\\in(1,2)\\). Under global Lipschitz continuity and dissipativity of the drift, we establish a Wasserstein-1 bound of order \\(m^{1/α}\\) between the invariant position distribution of the underdamped system and the invariant distribution of its overdamped limit, where $m>0$ is the mass parameter. The proof combines a corrected-position test function with a regularized Stein equation. Cancellation of the transport and friction terms reduces the comparison to a first-moment estimate for the stationary velocity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32217",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinghu Jin"
    },
    {
      "name": "Wenxuan Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52e0rnprk6bxp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32217",
  "fulltext_url": null,
  "id": "52e0rnprk6bxp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32217",
  "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"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223706024",
  "pdf_url": "https://arxiv.org/pdf/2610.32217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52e0rnprk6bxp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Wasserstein bounds for invariant measures in the Smoluchowski-Kramers approximation with stable noise",
  "title_text": "Wasserstein bounds for invariant measures in the Smoluchowski-Kramers approximation with stable noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/52e0rnprk6bxp",
  "venue": "arXiv",
  "versions": []
}