{"paper":{"title":"Universality for the largest eigenvalue of sample covariance matrices with general population","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Guangming Pan, Wang Zhou, Zhigang Bao","submitted_at":"2013-04-21T05:08:54Z","abstract_excerpt":"This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\\mathcal{W}_N=\\Sigma^{1/2}XX^*\\Sigma ^{1/2}$. Here, $X=(x_{ij})_{M,N}$ is an $M\\times N$ random matrix with independent entries $x_{ij},1\\leq i\\leq M,1\\leq j\\leq N$ such that $\\mathbb{E}x_{ij}=0$, $\\mathbb{E}|x_{ij}|^2=1/N$. On dimensionality, we assume that $M=M(N)$ and $N/M\\rightarrow d\\in(0,\\infty)$ as $N\\rightarrow\\infty$. For a class of general deterministic positive-definite $M\\times M$ matrices $\\Sigma$, under some additional a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5690","kind":"arxiv","version":8},"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"}