Asymptotic Lyapunov exponents for large random matrices

Hoi H. Nguyen

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arXiv · 1607.03172

Asymptotic Lyapunov exponents for large random matrices

Hoi H. Nguyen

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Abstract

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.

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Hoi H. Nguyen. 2016-07-11. Asymptotic Lyapunov exponents for large random matrices. https://arxiv.org/abs/1607.03172

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