  Several recent imaging experiments access the equilibrium density profiles of
interacting particles confined to a two-dimensional substrate. When these
particles are in a fluid phase, we show that such data yields precise
information regarding substrate disorder as reflected in one-point functions
and two-point correlations of the fluid. Using Monte Carlo simulations and
replica generalizations of liquid state theories, we extract unusual two-point
correlations of time-averaged density inhomogeneities induced by disorder.
Distribution functions such as these have not hitherto been measured but should
be experimentally accessible.
