Coupling the Totally Asymmetric Simple Exclusion Process with a Moving Interface
1998, v.4, Issue 4, 593-628
We explain a recently introduced coupling between the one-dimensional totally asymmetric simple exclusion process (TASEP) and a moving interface model. First we review how scaling limits can be obtained with this coupling. Secondly we prove new results about the large deviations of the interface model and the exclusion process. We derive the exact rate function for lower tail deviations of the interface, and for lower tail deviations of a tagged particle in the TASEP. The only assumption required on the initial distribution is that lower tail rate functions exist. We also show how deviations from the hydrodynamic limit that force particles to accelerate can decay exponentially in $n^2$ instead of the usual rate of exponential in $n$.
Keywords: exclusion process,hydrodynamic limit,tagged particle,large deviations,subadditive process,growth model,interface