{
  "abstract": "We study the skew-adjoint Hilbert--Schmidt operator obtained by evaluating a fixed Hilbert two-form on a centered Gaussian linear map whose covariance is the inner product on its domain multiplied by a fixed nonnegative trace-class operator. We compute the expected regularized determinant of the resulting random operator and compare the random determinant with this expectation by dilation of the scalar parameter. For each fixed covariance and two-form, a single dilation almost surely applies to every nonnegative parameter value and yields simultaneous bounds for all Schatten norms and quasi-norms of orders $0<p<2$. The least admissible dilation satisfies a universal weak-$L^1$ estimate with optimal tail exponent. For Wiener area, a rank-one perturbation identity identifies the mean determinant with the regularized determinant of an explicit deterministic skew-adjoint operator and reduces Schatten membership to conditions on the covariance eigenvalues. Consequently, for each $0<p<1$, the area belongs almost surely to the Schatten class of order $p$ if and only if the covariance of the Wiener process does. At $p=1$, the criterion is finite covariance entropy; for $p>1$, trace-class covariance suffices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34984",
  "author_total": 1,
  "authors": [
    {
      "name": "Guangqian Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a40pvqrraxfsx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34984",
  "fulltext_url": null,
  "id": "a40pvqrraxfsx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34984",
  "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",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7223821803",
  "pdf_url": "https://arxiv.org/pdf/2610.34984",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a40pvqrraxfsx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34984",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34984"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Gaussian Exterior Dilation and Schatten Classes of Lévy Area",
  "title_text": "Gaussian Exterior Dilation and Schatten Classes of Lévy Area",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/a40pvqrraxfsx",
  "venue": "arXiv",
  "versions": []
}