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We focus on the limiting regime $n,k \\to \\infty$ with $k = o(n)$, and we show that the limiting spectral distribution is the Mar\\v{c}enko-Pastur law. As a consequence, we show that the limiting spectral distribution of the Whishart matrix from the $k$-fold tensor product of independent uniformly distributed unit vectors in $\\mathbb C^n$ is the Mar\\v{c}enko-Pastur law.","authors_text":"Wangjun Yuan","cross_cats":[],"headline":"Sample correlation matrices from k-fold tensor vectors converge to the Marčenko-Pastur law when k grows slower than n.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-08T08:40:28Z","title":"On spectrum of sample correlation matrices from large fold tensor vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.06823","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T18:18:45.655757Z","id":"aad75aa9-4f81-4dcf-8b6c-1060dde5931b","model_set":{"reader":"grok-4.3"},"one_line_summary":"The limiting spectral distribution of sample correlation matrices from k-fold tensor vectors is the Marčenko-Pastur law when n, k → ∞ with k = o(n).","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Sample correlation matrices from k-fold tensor vectors converge to the Marčenko-Pastur law when k grows slower than n.","strongest_claim":"we show that the limiting spectral distribution is the Marčenko-Pastur law. 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