  We investigate the disorder dependence of the static density, amplitude and
current correlations within the attractive Hubbard model supplemented with
on-site disorder. It is found that strong disorder favors a decoupling of
density and amplitude correlations due to the formation of superconducting
islands. This emergent granularity also induces an enhancement of the density
correlations on the SC islands whereas amplitude fluctuations are most
pronounced in the 'insulating' regions. While density and amplitude
correlations are short-ranged at strong disorder we show that current
correlations have a long-range tail due to the formation of percolative current
paths in agreement with the constant behavior expected from the analysis of
one-dimensional models.
