Order of current variance and diffusivity in the asymmetric simple exclusion process

Abstract

We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary asymmetric simple exclusion process, and that the diffusivity has order t^{1/3}. The proof proceeds via couplings to show the corresponding results for the expected deviations and variance of a second class particle.

28 pages, revised version after referee's report. A picture is also added now