Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses

Abstract

We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

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References in corpus (3)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Moments of q-Normal and conditional q-Normal distributions
• Combinatorics of the asymmetric exclusion process on a semi-infinite lattice

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• Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
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• Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line