Asymptotic Lyapunov exponents for large random matrices

Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable ξof mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when ξis 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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