Exact tagged particle correlations in the random average process - art. no. 036103

We study analytically the correlations between the positions of tagged part icles in the random average process, an interacting particle system in one dimension. We show that in the steady state, the mean-squared autofluctuati on of a tracer particle grows subdiffusively sigma (2)(0)(t)similar tot(1/2 ) for large time t in the absence of external bias but grows diffusively si gma (2)(0)(t)similar tot 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 a lso compute sigma (2)(r)(t), the mean-squared fluctuation in the position d ifference of two tagged particles separated by a fixed tag shift r in the s teady state and show that the external bias has a dramatic effect on the ti me dependence of sigma (2)(r)(t). For fixed r,sigma (2)(r)(t) increases mon otonically 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.