Exact tagged particle correlations in the random average process

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 autofluctuation of a tracer particle grows subdiffusively ${\sigma }_0^2\mathrm{}\left(t\right)\mathrm{}\sim t^{1/2}$ for large time t in the absence of external bias but grows diffusively ${\sigma }_0^2\mathrm{}\left(t\right)\mathrm{}\sim t$ 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 ${\sigma }_r^2\mathrm{}\left(t\right),$ 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 on the time dependence of ${\sigma }_r^2\mathrm{}\left(t\right).$ For fixed $r,{\sigma }_r^2\mathrm{}\left(t\right)\mathrm{}$ increases monotonically with t in the absence of bias, but has a nonmonotonic dependence on t in the presence of bias. Similarities and differences with the simple exclusion process are also discussed.