Limit process of stationary TASEP near the characteristic line

The totally asymmetric simple exclusion process (TASEP) on\input amssym ${\Bbb Z}$ with the Bernoulli‐ρ measure as an initial condition, 0 < ρ < 1, is stationary. It is known that along the characteristic line, the current fluctuates at an order of t^1/3. The limiting distribution has also been obtained explicitly. In this paper we determine the limiting multipoint 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.