{
  "abstract": "We study convergence in Rényi divergence of order two for underdamped Langevin dynamics, the bouncy particle sampler, and the Zigzag sampler, for a target $e^{-U}$ on $\\mathbb R^d$ that satisfies a logarithmic Sobolev inequality, with $\\nabla^2U$ bounded below by a possibly negative constant and, for the Zigzag sampler, also bounded above. For initial laws whose Rényi divergence from equilibrium is at most $R$, we show that it decays exponentially, at a rate that depends on $R$. With the friction or refreshment rate chosen according to $R$, the time needed to reach a fixed accuracy in total variation or in Rényi divergence is of order $\\sqrt{R\\log R}$ at fixed dimension and target parameters, improving the linear dependence obtained by directly converting exponential $L^2$ decay. The key idea is to use the logarithmic Sobolev inequality for the position target in place of the usual spatial spectral-gap estimate in the $L^2$ hypocoercivity argument. For the bouncy particle and Zigzag samplers, this order is sharp for the Rényi divergence on a one-dimensional Gaussian target, uniformly in the refreshment rate. For the Zigzag sampler in dimension at least two, Gaussian examples show that the mixing-time bound is sharp up to logarithmic factors in the worst case over strongly convex targets, in both the initial divergence and the upper Hessian bound; in particular, strong convexity alone does not give a uniform mixing bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03921",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianfeng Lu"
    },
    {
      "name": "Yinchen Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1t8en69hnt1cr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03921",
  "fulltext_url": null,
  "id": "1t8en69hnt1cr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03921",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1t8en69hnt1cr.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Rényi mixing bounds for kinetic samplers via $L^2$ hypocoercivity",
  "title_text": "Rényi mixing bounds for kinetic samplers via L^2 hypocoercivity",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/1t8en69hnt1cr",
  "venue": "arXiv",
  "versions": []
}