The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-f measure as an initial condition, 0 < f< 1, is stationary. It is known that along the characteristic line, the current fluctuates at an order of t1=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 t2=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.
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