Abstract of "Limit process of stationary TASEP near the characteristic line"
with Jinho Baik and Sandrine Péché.
The totally asymmetric simple exclusion process (TASEP) on Z with the Bernoulli-ρ measure as initial conditions, 0<ρ<1, is stationary. It is known that along the characteristic line, the current fluctuates as of order t1/3. 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 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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