A rotation number calculation for Jacobi marices with matrix entries
is presented. This allows to derive a formula for the density of states
in the case of a random Jacobi matrix with matrix entries. In order
to evaluate the appearing Birkhoff sums perturbatively with a good
control of the error terms, a certain Fokker-Planck operator on the
symmetric space of Lagrangian planes is used. The latter result
follows from a general pertubative analysis of random Lie group
actions on compact Riemannian manifolds.