{
  "abstract": "We give faster algorithms for sampling from the uniform distribution over a polytope. Our main result is an algorithm that, when applied to a polytope with $m$ constraints in $n$ dimensions, uses $m \\cdot \\mathrm{poly}\\log(\\frac m δ)$ iterations, each running in time $O(mn^{ω- 1})$, to return a sample within total variation distance $δ$ to the uniform distribution. When $m =O(n)$ and $δ= \\mathrm{poly}(\\frac 1 n)$, our runtime improves upon all prior works by an $Ω(n^{2/3})$ factor. Our sampler is based on the recent \\emph{functional stochastic localization} framework of [GST26], and achieves an iteration count nearly matching the Poincaré constant of the uniform distribution with respect to the logarithmic barrier.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23775",
  "author_total": 4,
  "authors": [
    {
      "name": "Anming Gu"
    },
    {
      "name": "Bobby Shi"
    },
    {
      "name": "Kevin Tian"
    },
    {
      "name": "Hubert Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce77n4r2er489.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23775",
  "fulltext_url": null,
  "id": "ce77n4r2er489",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23775",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7222956479",
  "pdf_url": "https://arxiv.org/pdf/2610.23775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce77n4r2er489.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Polytope Sampling at the Speed of Isoperimetry",
  "title_text": "Polytope Sampling at the Speed of Isoperimetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/ce77n4r2er489",
  "venue": "arXiv",
  "versions": []
}