Superdiffusivity of Occupation-Time Variance in 2-dimensional Asymmetric Exclusion Processes with Density ρ = 1/2

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We compute that the growth of the occupation-time variance at the origin 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 give a complement to bounds in the literature when d = 1, and are consistent with an important conjecture with respect to the transition function and variance of “second-class” particles.

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