Blocks and Gaps in the Asymmetric Simple Exclusion Process: Asymptotics

Abstract

In earlier work (arXiv:1707.04927) 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 $t$. 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.

19 pages. Version 2 has a new title and an added section on asymptotics for gaps

References in corpus (6)

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• Asymptotics in ASEP with Step Initial Condition
• The one-dimensional KPZ equation and its universality class
• A Fredholm Determinant Representation in ASEP
• The crossover regime for the weakly asymmetric simple exclusion process
• Blocks in the Asymmetric Simple Exclusion Process