  We study fundamental spectral properties of random block operators that are
common in the physical modelling of mesoscopic disordered systems such as dirty
superconductors. Our results include ergodic properties, the location of the
spectrum, existence and regularity of the integrated density of states, as well
as Lifshits tails. Special attention is paid to the peculiarities arising from
the block structure such as the occurrence of a robust gap in the middle of the
spectrum. Without randomness in the off-diagonal blocks the density of states
typically exhibits an inverse square-root singularity at the edges of the gap.
In the presence of randomness we establish a Wegner estimate that is valid at
all energies. It implies that the singularities are smeared out by randomness,
and the density of states is bounded. We also show Lifshits tails at these band
edges. Technically, one has to cope with a non-monotone dependence on the
random couplings.
