On the asymmetric simple exclusion process with multiple species

TL;DR

This paper extends the analysis of the asymmetric simple exclusion process to multiple species with priority rules, deriving integral formulas for configuration probabilities and ensuring mathematical consistency via Yang-Baxter equations.

Contribution

It introduces a multi-species ASEP model with priority rules and derives integral formulas for its probabilities, verifying the Yang-Baxter equations for consistency.

Findings

Derived integral formulas for multi-species ASEP configurations

Established the role of Yang-Baxter equations in model consistency

Extended previous single-species results to multiple species

Abstract

In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves one step to the left if the site is unoccupied, otherwise it stays put. In previous work the authors, using the Bethe Ansatz, found for N-particle ASEP a formula --- a sum of multiple integrals --- for the probability that a system is in a particular configuration at time t given an initial configuration. The present work extends this to the case where particles are of different species, with particles of a higher species having priority over those of a lower species. Here the integrands in the multiple integrals are defined by a system of relations whose consistency requires verifying that the Yang-Baxter equations are satisfied.