{
  "abstract": "We study the complexity of approximating the finite-dimensional vector space embedding $\\ell_p^m \\hookrightarrow \\ell_q^m$ for $2 \\leq p < q \\leq \\infty$ based on non-adaptive randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance $x \\in \\mathbb{R}^m$, where $n \\ll m$. We prove lower bounds on the non-adaptive randomized approximation error with a joint dependence on $(n,m)$ matching previously known upper bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.00148",
  "author_total": 2,
  "authors": [
    {
      "name": "Robert J. Kunsch"
    },
    {
      "name": "Marcin Wnuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0z78qvgx9jeg5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.00148",
  "fulltext_url": null,
  "id": "0z78qvgx9jeg5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.00148",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7172441734",
  "pdf_url": "https://arxiv.org/pdf/2608.00148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0z78qvgx9jeg5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2608.00148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.00148"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Sharp bounds for non-adaptive randomized approximation of high-dimensional vectors",
  "title_text": "Sharp bounds for non-adaptive randomized approximation of high-dimensional vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/0z78qvgx9jeg5",
  "venue": "arXiv",
  "versions": []
}