{
  "abstract": "In randomised numerical linear algebra, common choices for distributions of sketch vectors $ω\\in \\mathbb R^n$ are isotropic, so that $\\mathbb E[ωω^T]=I_n$. Unfortunately, the natural extension of an isotropic vector in $(\\mathbb R^n, \\|\\cdot \\|_{2})$ to an infinite-dimensional separable Hilbert space $\\mathcal H$ may not exist as an element of the space, posing an obstacle for any attempt to lift the randomised SVD to infinite-dimensional target operators $A$. Current workarounds either forego isotropy and take $ω$ to be a continuous Gaussian process with trace-class covariance operators, or leave $ω$ implicit by instead sampling $Aω$ as if $ω$ were isotropic Gaussian. We unify their approaches by introducing \"sketch functionals\", an example of cylindrical random variables (Vakhania--Tarieladze--Chobanyan 1987) which allow us to treat general, non-Gaussian distributions with bounded covariance operators. To demonstrate the utility of the new theory, we apply it to develop novel bounds for the infinite-dimensional randomised SVD with a general class of sub-Gaussian sketch distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31333",
  "author_total": 2,
  "authors": [
    {
      "name": "Morgan Lynch-Davies"
    },
    {
      "name": "Marcus Webb"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38kdty3yphs2k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31333",
  "fulltext_url": null,
  "id": "38kdty3yphs2k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31333",
  "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|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7223344389",
  "pdf_url": "https://arxiv.org/pdf/2610.31333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38kdty3yphs2k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Sketching Outside the Hilbert Space for the Infinite-Dimensional Randomised SVD",
  "title_text": "Sketching Outside the Hilbert Space for the Infinite-Dimensional Randomised SVD",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/38kdty3yphs2k",
  "venue": "arXiv",
  "versions": []
}