{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2PHC37RVTLF4KWF72JMWWUHQCO","short_pith_number":"pith:2PHC37RV","schema_version":"1.0","canonical_sha256":"d3ce2dfe359acbc558bfd2596b50f013996c4c7ab6514ae6ac6c512ac710a105","source":{"kind":"arxiv","id":"1306.4277","version":1},"attestation_state":"computed","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 $ 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 $