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

Abstract

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.

Keywords

Asymmetric zero range process / diffusive scaling / spectral gap estimate / logarithmic Sobolev inequality

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