{"paper":{"title":"Extremal eigenvalues 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":"Jaewhi Park, Jinwoong Kwak, Ji Oon Lee","submitted_at":"2019-08-17T07:52:49Z","abstract_excerpt":"We consider the eigenvalues of sample covariance matrices of the form $\\mathcal{Q}=(\\Sigma^{1/2}X)(\\Sigma^{1/2}X)^*$. The sample $X$ is an $M\\times N$ rectangular random matrix with real independent entries and the population covariance matrix $\\Sigma$ is a positive definite diagonal matrix independent of $X$. Assuming that the limiting spectral density of $\\Sigma$ exhibits convex decay at the right edge of the spectrum, in the limit $M, N \\to \\infty$ with $N/M \\to d\\in(0,\\infty)$, we find a certain threshold $d_+$ such that for $d>d_+$ the limiting spectral distribution of $\\mathcal{Q}$ also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07444","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}