{
  "abstract": "We extend Seginer's matrix norm comparison to tensors with optimal dependence on the tensor order. For a real tensor $T$ of order $k\\ge2$ with centered, integrable, independent and identically distributed entries, we prove $\\mathbb{E} f(T)\\le\\mathbb{E}\\lVert T\\rVert_{\\mathrm{inj}} \\le C\\sqrt{k\\log k}\\,\\mathbb{E} f(T)$, where $f(T)$ is the largest Euclidean norm of a one-dimensional fiber and $C$ is universal. The comparison holds for every finite rectangular format, and the entry law may depend on both the dimensions and the tensor order. We show that the factor $\\sqrt{k\\log k}$ is optimal by considering Rademacher tensors on $[2]^k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39389",
  "author_total": 2,
  "authors": [
    {
      "name": "Ziqian Lin"
    },
    {
      "name": "Huangang Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/151wcajzq3kct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39389",
  "fulltext_url": null,
  "id": "151wcajzq3kct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39389",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39389",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/151wcajzq3kct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39389",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39389"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal fiber comparisons for random tensors",
  "title_text": "Optimal fiber comparisons for random tensors",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/151wcajzq3kct",
  "venue": "arXiv",
  "versions": []
}