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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2710","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-13T12:32:42Z","cross_cats_sorted":[],"title_canon_sha256":"75887265a29f955eec474a0981626deffeb7c2c7e86b8a89605185904e4d9519","abstract_canon_sha256":"ab658a0597ecdb97f16eac541bb4657b5e15bd66658b7fde1bea9dce4fed11b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:33.113485Z","signature_b64":"AlCxrPfWQ9fr/xcVDXEWMJjLIsK5AVz/XCFt3MbTs8jmN4ujfJsQtWs+h/xEpK36hA+ZTCFcfUWJ+3csvXX7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"211327ae12b10d2aeb0208c2c8fb2b8f788a55d1331f11789b527408c5c9222a","last_reissued_at":"2026-05-18T04:23:33.113013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:33.113013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\E {|X^{(\\nu)}_{jk}|}^2=1$. 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