{"paper":{"title":"Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2014-05-30T10:49:27Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le k\\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\\mathbf X$ to the semi-circular law assuming that ${\\mathbf E} X_{jk}=0$, ${\\mathbf E} X_{jk}^2=1$ and that $$ \\sup_{n\\ge1}\\sup_{1\\le j,k\\le n}{\\mathbf E}|X_{jk}|^4=:\\mu_4<\\infty \\quad \\text{and} \\sup_{1\\le j,k\\le n}|X_{jk}|\\le D_0n^{\\frac14}. $$ By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7820","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"}