Equilibrium fluctuations for the totally asymmetric zero-range process

Abstract

We consider the one-dimensional Totally Asymmetric Zero-Range process evolving on $\mathbb{Z}$ and starting from the Geometric product measure $\mu_\rho$. On the hyperbolic time scale the temporal evolution of the density fluctuation field is deterministic, in the sense that the limit field at time $t$ is a translation of the initial one. We consider the system in a reference frame moving at this velocity and we show that the limit density fluctuation field does not evolve in time until $N^{4/3}$, which implies the current across a characteristic to vanish on this longer time scale.