Order of current variance and diffusivity in the rate one totally asymmetric zero range process
Abstract
We prove that the variance of the current across a characteristic is of order t2/3 in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t1/3. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave hydrodynamic flux. The proof proceeds via couplings to show the corresponding moment bounds for a second class particle. We build on the methods developed by Balazs-Seppalainen for asymmetric simple exclusion. However, some modifications were needed to handle the larger state space. Our results translate into t2/3-order of variance of the tagged particle on the characteristics of totally asymmetric simple exclusion.