Abstract of "Limit law of a second class particle in TASEP with non-random initial condition"
with Peter Nejjar and Promit Ghosal.
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density λ on Z− and ρ on Z+, and a second class particle initially at the origin. For λ < ρ there is a shock and the second class particle moves with speed 1 − ρ - λ . For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.
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