  In a previous contribution (H.J. Stoeckmann, J. Phys. A35, 5165 (2002)), the
density of states was calculated for a billiard with randomly distributed
delta-like scatterers, doubly averaged over the positions of the impurities and
the billiard shape. This result is now extended to the k-point correlation
function. Using supersymmetric methods, we show that the correlations in the
bulk are always identical to those of the Gaussian Unitary Ensemble (GUE) of
random matrices. In passing from the band centre to the tail states, The
density of states is depleted considerably and the two-point correlation
function shows a gradual change from the GUE behaviour to that found for
completely uncorrelated eigenvalues. This can be viewed as similar to a
mobility edge.
