The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-rho measure as initial conditions, 0<rho<1, is stationary. It is known that along the characteristic line, the current fluctuates as of order t^{ 1/3}. The limiting distribution has also been obtained explicitly. In this paper we determine the limiting multi-point distribution of the current fluctuations moving away from the characteristics by the order t^{ 2/3}. The main tool is the analysis of a related directed last percolation model. We also discuss the process limit in tandem queues in equilibrium.
Categories: math-ph cond-mat.stat-mech math.CO math.MP