{"paper":{"title":"Asymptotic properties of eigenmatrices of a large sample covariance matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"H. X. Liu, W. K. Wong, Z. D. Bai","submitted_at":"2011-12-30T09:12:40Z","abstract_excerpt":"Let $S_n=\\frac{1}{n}X_nX_n^*$ where $X_n=\\{X_{ij}\\}$ is a $p\\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\\mathbf {t}_1,\\mathbf {t}_2,\\sigma)=\\sqrt{p}({\\mathbf {x}}_n(\\mathbf {t}_1)^*(S_n+\\sigma I)^{-1}{\\mathbf {x}}_n(\\mathbf {t}_2)-{\\mathbf {x}}_n(\\mathbf {t}_1)^*{\\mathbf {x}}_n(\\mathbf {t}_2)m_n(\\sigma))$ in which $\\sigma>0$ and $m_n(\\sigma)=\\int\\frac{dF_{y_n}(x)}{x+\\sigma}$ where $F_{y_n}(x)$ is the Mar\\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\\to\\infty$, and ${\\mathbf {x}}_n(\\mathbf {t}_1)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0086","kind":"arxiv","version":1},"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"}