{"paper":{"title":"Lyapunov exponents and eigenvalues of products of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Nanda Kishore Reddy","submitted_at":"2016-06-24T14:35:22Z","abstract_excerpt":"Let $X_1,X_2, \\ldots $ be a sequence of $i.i.d$ real (complex) $d \\times d $ invertible random matrices with common distribution $\\mu$ and $\\sigma_1(n), \\sigma_2(n), \\ldots , \\sigma_d(n)$ be the singular values, $\\lambda_1(n), \\lambda_2(n), \\ldots , \\lambda_d(n)$ be the eigenvalues of $X_nX_{n-1}\\cdots X_1$ in the decreasing order of their absolute values for every $n$. It is known that if $\\mathbb{E}(\\log^{+}\\|X_1\\|)< \\infty$, then with probability one for all $1 \\leq p \\leq d$, $$\n  \\lim_{n \\to \\infty} \\frac{1}{n}\\log \\sigma_p(n)=\\gamma_p, $$ where ${\\gamma_1,\\gamma_2 \\ldots \\gamma_d}$ are t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07704","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"}