{"paper":{"title":"Rate of Convergence of the Expected Spectral Distribution Function to the Marchenko -- Pastur Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.N. Tikhomirov, F. G\\\"otze","submitted_at":"2014-12-19T10:49:21Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})$ denote a $n\\times p$ random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le n, 1\\le k\\le p$. Let $n,p$ tend to infinity such that $\\frac np=y+O(n^{-1})\\in(0,1]$. For those values of $n,p$ we investigate the rate of convergence of the expected spectral distribution function of the matrix $\\mathbf W=\\frac1{ p}\\mathbf X\\mathbf X^*$ to the Marchenko-Pastur law with parameter $y$. Assuming the conditions $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and $ \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\sup_{n,p\\ge1}\\sup_{1\\le j\\le n,1\\le k\\le p}\\mathbf E |X_{jk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6284","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"}