Limiting current distribution for a two species asymmetric exclusion process

TL;DR

This paper analyzes current fluctuations in a two-species asymmetric exclusion process, deriving explicit formulas and showing that, over time, the distribution converges to a product of Gaussian and Tracy-Widom distributions, confirming hydrodynamic predictions.

Contribution

It provides an explicit integral formula for joint current distributions and proves their asymptotic form as a product of Gaussian and Tracy-Widom distributions.

Findings

Joint current distribution expressed as a multiple integral.

Asymptotic distribution is a product of Gaussian and GUE Tracy-Widom.

Results confirm predictions of non-linear fluctuating hydrodynamics.

Abstract

We study current fluctuations of a two-species 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.