  We study analytically the correlations between the positions of tagged
particles in the random average process, an interacting particle system in one
dimension. We show that in the steady state the mean squared auto-fluctuation
of a tracer particle grows subdiffusively as $sigma^2(t) ~ t^{1/2}$ for large
time t in the absence of external bias, but grows diffusively $sigma^2(t) ~ t$
in the presence of a nonzero bias. The prefactors of the subdiffusive and
diffusive growths as well as the universal scaling function describing the
crossover between them are computed exactly. We also compute $sigma_r^2(t)$,
the mean squared fluctuation in the position difference of two tagged particles
separated by a fixed tag shift r in the steady state and show that the external
bias has a dramatic effect in the time dependence of $sigma_r^2(t)$. For fixed
r, $sigma_r^2(t)$ increases monotonically with t in absence of bias but has a
non-monotonic dependence on t in presence of bias. Similarities and differences
with the simple exclusion process are also discussed.
