  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.
