The distribution of Lyapunov exponents: Exact results for random matrices

Simple exact expressions are derived for all the Lyapunov exponents of certainN-dimensional stochastic linear dynamical systems. In the case of the product of independent random matrices, each of which has independent Gaussian entries with mean zero and variance 1/N, the exponents have an exponential distribution asN. In the case of the time-ordered product integral of expN ^–1/2 dW], where the entries of theN×N matrixW(t) are independent standard Wiener processes, the exponents are equally spaced for fixedN and thus have a uniform distribution as N.John S. Guggenheim Memorial Fellow. Research supported in part by NSF Grant MCS 80-19384