{
  "abstract": "We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting cumulant bounds are asymptotically sharp and yield lower bounds for Gaussian entropy deficits. We also establish quantitative versions of sharp min-entropy power inequalities in all dimensions. En route, we develop a stability result for Brzezinski's sharp bound for block sections of products of Euclidean balls, which may be of independent interest.",
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  "article_type": null,
  "arxiv": "2609.22065",
  "author_total": 3,
  "authors": [
    {
      "name": "Silouanos Brazitikos"
    },
    {
      "name": "Martin Rapaport"
    },
    {
      "name": "Tomasz Tkocz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cs1se154cfcsd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22065",
  "fulltext_url": null,
  "id": "cs1se154cfcsd",
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  "landing_url": "https://arxiv.org/abs/2609.22065",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "cs.IT"
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      "arxiv",
      "math.FA"
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  "pdf_url": "https://arxiv.org/pdf/2609.22065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cs1se154cfcsd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.22065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Hermite-Fisher bounds and stability for min-entropy power inequalities",
  "title_text": "Hermite-Fisher bounds and stability for min-entropy power inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/cs1se154cfcsd",
  "venue": "arXiv",
  "versions": []
}