Tracy-Widom limit of q-Hahn TASEP

TL;DR

This paper proves that the current fluctuations in the q-Hahn TASEP, a generalized particle system, follow the Tracy-Widom distribution, confirming the KPZ universality class for this model.

Contribution

It establishes the Tracy-Widom limit for the q-Hahn TASEP, extending the understanding of fluctuation behavior in this class of interacting particle systems.

Findings

Current fluctuations are of order t^{1/3}

Fluctuations asymptotically follow GUE Tracy-Widom distribution

Confirms the KPZ scaling theory conjecture for q-Hahn TASEP

Abstract

We consider the q-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain q-Binomial distribution with parallel updates. It is a generalization of the discrete time q-TASEP which is the q-deformed totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1). For step initial condition, we prove that the current fluctuation of q-Hahn TASEP at time t is of order $t^{1/3}$ and asymptotically distributed as the GUE Tracy-Widom distribution. We verify the KPZ scaling theory conjecture for the q-Hahn TASEP.