{
  "abstract": "We study the moments of sample covariance matrices $M_{n,k,m}$ formed from independent $k$-fold tensor products of $n$-dimensional random vectors. The base vectors have independent and identically distributed centered complex entries with unit variance and finite moments of all orders. For every fixed $p \\in \\mathbb N_+$, under suitable moment conditions, we obtain an asymptotic formula for $p$th moment as $n, k, m$ tend to infinity with $m/n^k \\to c \\in (0,\\infty)$. There is no restriction on the growth rate of $k$ relative to $n$. We also prove a variance bound and obtain the corresponding almost sure asymptotic formula. The results recover known limiting moments in several regimes. When $k/n$ tends to infinity and the modulus of base vector entry is not constant, we establish the asymptotic growth rate for the $p$th moment of normalized matrices. In this regime, we also provide a lower bound for the growth rate of the largest eigenvalue.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33687",
  "author_total": 1,
  "authors": [
    {
      "name": "Wangjun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6z9vz0dsa05c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33687",
  "fulltext_url": null,
  "id": "f6z9vz0dsa05c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33687",
  "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": "W7224004173",
  "pdf_url": "https://arxiv.org/pdf/2610.33687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6z9vz0dsa05c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33687"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limiting moments of sample covariance matrices from large fold tensor vectors",
  "title_text": "Limiting moments of sample covariance matrices from large fold tensor vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/f6z9vz0dsa05c",
  "venue": "arXiv",
  "versions": []
}