{
  "abstract": "We prove that an operator-norm separated family of matrices satisfies $\\mathbb{E}\\sup_{A\\in T} G^{T}AG' \\geq ca\\log |T|$, where G,G' are independent standard Gaussian vectors and a is the separation. The main information estimate concerns arbitrary separated coisometries: conditional entropy is bounded by a source-dependent operator energy times $\\log|T|$, up to an additive quadratic term in the common row dimension. An adaptive Gaussian experiment proves this estimate by charging actual information increments to one weighted posterior-entropy potential. Convex separation and a Gaussian covering estimate then yield a bounded-radius result. To reach the general case, we first choose an operator scale preserving the Sudakov ratio, apply the known Hilbert-Schmidt minoration, and recompute a common Gaussian block compression at the retained entropy. This ordering preserves the normalization needed by the coisometry argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23558",
  "author_total": 3,
  "authors": [
    {
      "name": "Witold Bednorz"
    },
    {
      "name": "Rafał Martynek"
    },
    {
      "name": "Rafał Meller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7z35abs9q4eec.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23558",
  "fulltext_url": null,
  "id": "7z35abs9q4eec",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23558",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214011507",
  "pdf_url": "https://arxiv.org/pdf/2609.23558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7z35abs9q4eec.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.23558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Operator-norm Sudakov minoration for Gaussian chaos of order two",
  "title_text": "Operator-norm Sudakov minoration for Gaussian chaos of order two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7z35abs9q4eec",
  "venue": "arXiv",
  "versions": []
}