Distribution of a Second-Class Particle’s Position in the Two-Species ASEP with a Special Initial Configuration

Abstract

In this paper, we consider the two-species asymmetric simple exclusion process (ASEP) consisting of N-1 first-class particles and one second-class particle. We assume that all particles are located at arbitrary positions but the second-class particle is the rightmost particle at time t = 0. We find the exact formula of the distribution of the second-class particle’s position at time t by directly using the transition probabilities of the two-species ASEP, which is a different approach from the coupling method Tracy and Widom used in [J Phys A 42:425002, 2009].