Tracy-Widom limit of q-Hahn TASEP

Understand

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.