  We expose a functional integration method for the averaging of continuous
products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we
compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. 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.
