Blocks in the Asymmetric Simple Exclusion Process

Abstract

In earlier work the authors obtained formulas for the probability in the asymmetric simple exclusion process that the $m$th particle from the left is at site $x$ at time $t$. They were expressed in general as sums of multiple integrals and, for the case of step initial condition, as an integral involving a Fredholm determinant. In the present work these results are generalized to the case where the $m$th particle is the left-most one in a contiguous block of $L$ particles. The earlier work depended in a crucial way on two combinatorial identities, and the present work begins with a generalization of these identities to general $L$.

17 pages. Version 2 elaborates on a point overlooked in Version 1

References in corpus (6)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Asymptotics in ASEP with Step Initial Condition
• Integral Formulas for the Asymmetric Simple Exclusion Process
• A Fredholm Determinant Representation in ASEP
• The crossover regime for the weakly asymmetric simple exclusion process
• Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process

Cited by in corpus (2)

• Blocks and Gaps in the Asymmetric Simple Exclusion Process: Asymptotics
• Blocks in ASEP with step-Bernoulli initial condition