{
  "abstract": "We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target $π\\propto e^{-V}$, where $0 \\prec αI\\preceq\\nabla^2V\\preceqβI$ and $κ=β/α$. To achieve $\\sqrtα\\,W_2\\leqslant\\varepsilon$, we show that deterministic Heun uses at most $\\widetilde O(κ^{4/3}d^{1/3}\\varepsilon^{-2/3})$ gradient queries, and underdamped exponential midpoint uses $\\widetilde O(κ^{5/4}d^{1/4}\\varepsilon^{-1/2})$. The proofs exploit cancellation at stationarity and smoothing using techniques from Malliavin calculus, outperforming previous upper bounds based on standard couplings. At bounded condition number, a lower bound matches the $d$ and $\\varepsilon$ powers of both deterministic methods. To contrast, for the randomized midpoint methods and Poisson midpoint with at least two grid points (both overdamped and underdamped variants), a simple Gaussian calculation yields a lower bound $d^{1/3}\\varepsilon^{-1/3}$ to get an $\\varepsilon$-close sample despite starting at a benign initialization. This shows surprisingly that in high dimensions, deterministic discretizations can outperform their random counterparts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06308",
  "author_total": 4,
  "authors": [
    {
      "name": "Fan Chen"
    },
    {
      "name": "Sinho Chewi"
    },
    {
      "name": "Jianfeng Lu"
    },
    {
      "name": "Matthew S. Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/086jc8p42yk86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06308",
  "fulltext_url": null,
  "id": "086jc8p42yk86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06308",
  "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",
      "cs.DS"
    ],
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      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
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      "arxiv",
      "math.ST"
    ],
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      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7220727458",
  "pdf_url": "https://arxiv.org/pdf/2610.06308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/086jc8p42yk86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Sharp dimensional analysis of midpoint methods for Langevin sampling",
  "title_text": "Sharp dimensional analysis of midpoint methods for Langevin sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/086jc8p42yk86",
  "venue": "arXiv",
  "versions": []
}