Superdiffusivity of occupation - time variance in 2 - dimensional asymmetric exclusion processes with density

We compute that the growth of the origin occupation-time variance up to time t in dimension d = 2 with respect to asymmetric simple exclusion in equilibrium with density ρ = 1/2 is in a certain sense at least t log(log t) for general rates, and at least t(log t)1/2 for rates which are asymmetric only in the direction of one of the axes. These estimates are consistent with an important conjecture with respect to the transition function and variance of “second-class” particles. Abbreviated title: Occupation-time variance in 2D asymmetric exclusion process with density 1/2 AMS (2000) subject classifications: Primary 60K35; secondary 60F05.