Blocks and gaps in the asymmetric simple exclusion process: Asymptotics

In earlier work, the authors obtained formulas for the probability in the asymmetric simple exclusion process that at time t, a particle is at site x and is the beginning of a block of L consecutive particles. Here we consider asymptotics. Specifically, for the Kardar-Parisi-Zhang regime with step initial condition, we determine the conditional probability (asymptotically as t -> infinity) that a particle is the beginning of an L-block, given that it is at site x at time t. Using duality between occupied and unoccupied sites, we obtain the analogous result for a gap of G unoccupied sites between the particle at x and the next one. Published by AIP Publishing.