{"paper":{"title":"Asymptotic Lyapunov exponents for large random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Hoi H. Nguyen","submitted_at":"2016-07-11T21:30:35Z","abstract_excerpt":"Suppose that A_1,\\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \\xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \\xi is gaussian then N^{-1} \\log ||A_N \\dots A_1|| converges to a non-random limit. We extend this result to more general matrices with explicit rate of convergence. Our method relies on a simple connection between structures and dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03172","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"}