{"paper":{"title":"Eigenvectors of Sample Covariance Matrices: Universality of global fluctuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ali Bouferroum","submitted_at":"2013-06-18T17:40:40Z","abstract_excerpt":"In this paper, we prove a universality result of convergence for a bivariate random process defined by the eigenvectors of a sample covariance matrix. Let $V_n=(v_{ij})_{i \\leq n,\\, j\\leq m}$ be a $n\\times m$ random matrix, where $(n/m)\\to y > 0$ as $ n \\to \\infty$, and let $X_n=(1/m) V_n V^{*}_n $ be the sample covariance matrix associated to $V_n \\:$. Consider the spectral decomposition of $X_n$ given by $ U_n D_n U_n^{*}$, where $U_n=(u_{ij})_{n\\times n}$ is an eigenmatrix of $X_n$. We prove, under some moments conditions, that the bivariate random process $<B_{s,t}^{n} = \\underset{1\\leq j "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4277","kind":"arxiv","version":1},"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"}