  We study the density of states measure for some class of random unitary band
matrices and prove a Thouless formula relating it to the associated Lyapunov
exponent. This class of random matrices appears in the study of the dynamical
stability of certain quantum systems and can also be considered as a unitary
version of the Anderson model. We further determine the support of the density
of states measure and provide a condition ensuring it possesses an analytic
density.
