  The steady state reached by a system of particles sliding down a fluctuating
surface has interesting properties. Particle clusters form and break rapidly,
leading to a broad distribution of sizes and large fluctuations. The
density-density correlation function is a singular scaling function of the
separation and system size. A simple mapping is shown to take a configuration
of sliding hard-core particles with mutual exclusion (a system which shows a
cusp singularity) to a configuration with multiparticle occupancy. For the
mapped system, a calculation of the correlation function shows that it is of
the same scaling form again, but with a stronger singularity (a divergence) of
the sort observed earlier for noninteracting passive particles.
