Equilibrium Perturbations for the Asymmetric Zero Range Process Under Diffusive Scaling in Dimensions d ≥ 2

We consider the asymmetric zero range process in dimensions d ≥ 2. Assume the initial density profile is a perturbation of the constant density, which has order N^−α, α ∈ (0, 1), and is constant along the drift direction. Here, N is the scaling parameter. We show that under some constraints on the jump rate of the zero range process, the perturbed quantity macroscopically obeys the heat equation under diffusive scaling.