The crossover regime for the weakly asymmetric simple exclusion process

Understand

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition.

• Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location.
• One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations.
• The appropriate crossover scale is an asymmetry of order $\epsilon^{-1/2}$, times of order $\epsilon^{-2}$, and a spatial location of order $\epsilon^{-3/2}$.