{"paper":{"title":"Universality of covariance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jun Yin, Natesh S. Pillai","submitted_at":"2011-10-11T20:23:41Z","abstract_excerpt":"In this paper we prove the universality of covariance matrices of the form $H_{N\\times N}={X}^{\\dagger}X$ where $X$ is an ${M\\times N}$ rectangular matrix with independent real valued entries $x_{ij}$ satisfying $\\mathbb{E}x_{ij}=0$ and $\\mathbb{E}x^2_{ij}={\\frac{1}{M}}$, $N$, $M\\to \\infty$. Furthermore it is assumed that these entries have sub-exponential tails or sufficiently high number of moments. We will study the asymptotics in the regime $N/M=d_N\\in(0,\\infty),\\lim_{N\\to\\infty}d_N\\neq0,\\infty$. Our main result is the edge universality of the sample covariance matrix at both edges of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2501","kind":"arxiv","version":7},"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"}