{"paper":{"title":"CLT for linear eigenvalue statistics for a tensor product version of sample covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Lytova","submitted_at":"2016-02-27T17:12:35Z","abstract_excerpt":"For $k,m,n\\in \\mathbb{N}$, we consider $n^k\\times n^k$ random matrices of the form $$ \\mathcal{M}_{n,m,k}(\\mathbf{y})=\\sum_{\\alpha=1}^m\\tau_\\alpha {Y_\\alpha}Y_\\alpha^T,\\quad Y_\\alpha=\\mathbf{y}_\\alpha^{(1)}\\otimes...\\otimes\\mathbf{y}_\\alpha^{(k)}, $$ where $\\tau _{\\alpha }$, $\\alpha\\in[m]$, are real numbers and $\\mathbf{y}_\\alpha^{(j)}$, $\\alpha\\in[m]$, $j\\in[k]$, are i.i.d. copies of a normalized isotropic random vector $\\mathbf{y}\\in \\mathbb{R}^n$. For every fixed $k\\ge 1$, if the Normalized Counting Measures of $\\{\\tau _{\\alpha }\\}_{\\alpha}$ converge weakly as $m,n\\rightarrow \\infty$, $m/n^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08613","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}