{
  "abstract": "Let $μ(d x)\\propto e^{-U(x)} d x$ on $\\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $κ=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate. Combining this construction with quantitative mixing estimates and finite-time bounds on the expected numbers of bounces and flips yields query complexity guarantees from a Gaussian cold start. For total-variation error $\\varepsilon$, the expected query counts are $O(κ^{1/2}d\\,(d\\logκ+\\log\\frac1\\varepsilon))$ gradient queries for the bouncy particle sampler and $O(κd^{1/4}(d\\logκ+\\log\\frac1\\varepsilon))$ full-gradient equivalents for Zigzag, where $d$ coordinate-partial queries count as one equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28413",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianfeng Lu"
    },
    {
      "name": "Yinchen Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7qvxcpkmyf6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28413",
  "fulltext_url": null,
  "id": "f7qvxcpkmyf6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28413",
  "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": [
    [
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      "cs.LG"
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      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
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  "openalex": "W7171970386",
  "pdf_url": "https://arxiv.org/pdf/2607.28413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7qvxcpkmyf6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2607.28413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Windowed thinning and query complexity for the bouncy particle and Zigzag samplers",
  "title_text": "Windowed thinning and query complexity for the bouncy particle and Zigzag samplers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:26Z",
  "url": "https://research.draconitic.com/paper/f7qvxcpkmyf6q",
  "venue": "arXiv",
  "versions": []
}