{"paper":{"title":"No outliers in the spectrum of the product of independent non-Hermitian random matrices with independent entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuriy Nemish","submitted_at":"2014-12-07T23:05:06Z","abstract_excerpt":"We consider products of independent square random non-Hermitian matrices. More precisely, let $n\\geq 2$ and let $X_1,\\ldots,X_n$ be independent $N\\times N$ random matrices with independent centered entries with variance $N^{-1}$. It was shown by G\\\"otze and Tikhomirov and by Soshnikov and O'Rourke that the limit of the empirical spectral distribution of the product $X_1\\cdots X_n$ is supported in the unit disk. We prove that if the entries of the matrices $X_1,\\ldots,X_n$ satisfy uniform subexponential decay condition, then the spectral radius of $X_1\\cdots X_n$ converges to 1 almost surely as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2410","kind":"arxiv","version":2},"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"}