The Lyapunov spectrum of a continuous product of random matrices

We present a functional integration method for the averaging of continuous products <(P)over cap t> of NxN random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of (P) over cap(t)$. This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white-noise force field.