Blocks in the Asymmetric Simple Exclusion Process: Asymptotics

Craig A. Tracy, Harold Widom

Published 2017-11-22Version 1

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 KPZ regime with step initial condition, we determine the conditional probability (asymptotically as $t\to\infty$) that a particle is the beginning of an $L$-block, given that it is at site $x$ at time $t$.