{"paper":{"title":"A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fan Yang, Xiucai Ding","submitted_at":"2016-07-23T01:19:38Z","abstract_excerpt":"In this paper, we prove a necessary and sufficient condition for the edge universality of sample covariance matrices with general population. We consider sample covariance matrices of the form $\\mathcal Q = TX(TX)^{*}$, where the sample $X$ is an $M_2\\times N$ random matrix with $i.i.d.$ entries with mean zero and variance $N^{-1}$, and $T$ is an $M_1 \\times M_2$ deterministic matrix satisfying $T^* T$ is diagonal. We study the asymptotic behavior of the largest eigenvalues of $\\mathcal Q$ when $M:=\\min\\{M_1,M_2\\}$ and $N$ tends to infinity with $\\lim_{N \\to \\infty} {N}/{M}=d \\in (0, \\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06873","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"}