{"paper":{"title":"Limiting spectral distribution of renormalized separable sample covariance matrices when $p/n\\to 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Debashis Paul, Lili Wang","submitted_at":"2013-08-08T06:33:05Z","abstract_excerpt":"We are concerned with the behavior of the eigenvalues of renormalized sample covariance matrices of the form C_n=\\sqrt{\\frac{n}{p}}\\left(\\frac{1}{n}A_{p}^{1/2}X_{n}B_{n}X_{n}^{*}A_{p}^{1/2}-\\frac{1}{n}\\tr(B_{n})A_{p}\\right) as $p,n\\to \\infty$ and $p/n\\to 0$, where $X_{n}$ is a $p\\times n$ matrix with i.i.d. real or complex valued entries $X_{ij}$ satisfying $E(X_{ij})=0$, $E|X_{ij}|^2=1$ and having finite fourth moment. $A_{p}^{1/2}$ is a square-root of the nonnegative definite Hermitian matrix $A_{p}$, and $B_{n}$ is an $n\\times n$ nonnegative definite Hermitian matrix. We show that the empir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1766","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"}