  We consider an m-dimensional analytic cocycle with underlying dynamics given
by an irrational translation on the circle. Assuming that the d-dimensional
upper left corner of the cocycle is typically large enough, we prove that the d
largest Lyapunov exponents associated with this cocycle are bounded away from
zero. The result is uniform relative to certain measurements on the matrix
blocks forming the cocycle. As an application of this result, we obtain
nonperturbative (in the spirit of Sorets-Spencer theorem) positive lower bounds
of the nonnegative Lyapunov exponents for various models of band lattice
Schroedinger operators.
