  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.
