{"paper":{"title":"On the Rate of Convergence to the Marchenko--Pastur Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2011-10-06T14:52:33Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})$ denote $n\\times p$ random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le n,1\\le k\\le p$. We consider the rate of convergence of empirical spectral distribution function of the matrix $\\mathbf W=\\frac1p\\mathbf X\\mathbf X^*$ to the Marchenko--Pastur law. We assume that $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and that the distributions of the matrix elements $X_{jk}$ have a uniformly sub exponential decay in the sense that there exists a constant $\\varkappa>0$ such that for any $1\\le j \\le n,\\,1\\le k\\le p $ and any $t\\ge 1$ we have $$ \\mathbf{ Pr}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1284","kind":"arxiv","version":3},"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"}