Limiting Current Distribution for a Two Species Asymmetric Exclusion Process

We study current fluctuations of a two-species totally asymmetric exclusion process, known as the Arndt–Heinzel–Rittenberg model. For a step-Bernoulli initial condition with finite number of particles, we provide an explicit multiple integral expression for a certain joint current probability distribution. By performing an asymptotic analysis we prove that the joint current distribution is given by a product of a Gaussian and a GUE Tracy–Widom distribution in the long time limit, as predicted by non-linear fluctuating hydrodynamics.