{"paper":{"title":"On the Asymptotic Spectrum of Products of Independent Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Tikhomirov, Friedrich G\\\"otze","submitted_at":"2010-12-13T12:32:42Z","abstract_excerpt":"We consider products of independent random matrices with independent entries. The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let $X^{(\\nu)}_{jk},{}1\\le j,r\\le n$, $\\nu=1,...,m$ be mutually independent complex random variables with $\\E X^{(\\nu)}_{jk}=0$ and $\\E {|X^{(\\nu)}_{jk}|}^2=1$. Let $\\mathbf X^{(\\nu)}$ denote an $n\\times n$ matrix with entries $[\\mathbf X^{(\\nu)}]_{jk}=\\frac1{\\sqrt{n}}X^{(\\nu)}_{jk}$, for $1\\le j,k\\le n$.\n  Denote by $\\lambda_1,...,\\lambda_n$ the eigenvalues of the random matrix $\\mathbf W:= \\prod_{\\nu=1}^m\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2710","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"}