{"paper":{"title":"Edge universality of correlation 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":"2011-12-11T18:27:08Z","abstract_excerpt":"Let $\\widetilde{X}_{M\\times N}$ be a rectangular data matrix with independent real-valued entries $[\\widetilde{x}_{ij}]$ satisfying $\\mathbb {E}\\widetilde{x}_{ij}=0$ and $\\mathbb {E}\\widetilde{x}^2_{ij}=\\frac{1}{M}$, $N,M\\to\\infty$. These entries have a subexponential decay at the tails. We will be working in the regime $N/M=d_N,\\lim_{N\\to\\infty}d_N\\neq0,1,\\infty$. In this paper we prove the edge universality of correlation matrices ${X}^{\\dagger}X$, where the rectangular matrix $X$ (called the standardized matrix) is obtained by normalizing each column of the data matrix $\\widetilde{X}$ by it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2381","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":""},"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"}