We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process with nearest-neighbor-jumps diverges as (log t)2/3 to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes. 1. Introduction The asymmetric simple exclusion process is a Markov process on {0, 1}Z with asymmetric jump rates. There is at most one particle allowed per site and thus the word exclusion. The particle at a site x waits for an exponential time and then jumps to y with rate p(x − y) provided that the site is not occupied. .
