  We study the fluctuations of particles sliding on a stochastically growing
surface. This problem can be mapped to motion of passive scalars in a randomly
stirred Burger's flow. Renormalization group studies, simulations, and scaling
arguments in one dimension, suggest a rich set of phenomena: If particles slide
with the avalanche of growth sites (advection with the fluid), they tend to
cluster and follow the surface dynamics. However, for particles sliding against
the avalanche (anti-advection), we find slower diffusion dynamics, and density
fluctuations with no simple relation to the underlying fluid, possibly with
continuously varying exponents.
