{
  "abstract": "We study the number of exact matrix-vector queries needed to sample a centered $d$-dimensional Gaussian with condition number at most $κ$ to total variation error $\\varepsilon$. The best known algorithm uses $O(\\min\\{d,\\sqrtκ\\log(\\frac{d}{\\varepsilon})\\})$ queries, while the known lower bounds do not grow as $\\varepsilon\\to0$ and match this bound only for $κ\\le d^{1/5-δ}$ at constant accuracy. We introduce a construction based on a hidden determinant sign and prove a lower bound of $Ω\\!\\left(\\min\\left\\{d,\\sqrtκ\\log\\left(1+\\frac{d}{\\sqrtκ\\,\\varepsilon}\\right)\\right\\}\\right)$ uniformly for all $d\\ge1$, $κ\\ge4$, and $0<\\varepsilon\\le\\tfrac{1}{16}$. This bound matches the known upper bound up to constant factors whenever $κ\\le d^{2-δ}$ for fixed $δ\\in(0,2)$, or $\\varepsilon\\le d^{-c}$ for fixed $c>0$. We also extend a recent fixed-spectrum construction with a hidden eigenbasis from $κ=2$ to $2\\leκ\\le d^{1-δ}$, for any fixed $δ\\in(0,1)$. This gives an $Ω_δ(\\sqrtκ\\log d)$ lower bound at constant accuracy that holds even when the spectrum of the precision matrix is known to the algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20492",
  "author_total": 2,
  "authors": [
    {
      "name": "Huanjian Zhou"
    },
    {
      "name": "Taiji Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zq049q7enf6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20492",
  "fulltext_url": null,
  "id": "1zq049q7enf6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20492",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7222034837",
  "pdf_url": "https://arxiv.org/pdf/2610.20492",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zq049q7enf6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.20492",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20492"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "On Complexity of Gaussian Sampling",
  "title_text": "On Complexity of Gaussian Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/1zq049q7enf6s",
  "venue": "arXiv",
  "versions": []
}