A central limit theorem for reversible exclusion and zero-range particle systems

We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let η(t) be the configuration of the process at time t and let f(η) be a function on the state space. The question is: For which functions f does λ ^-1/2∫^λt₀ f(η(s)) ds converge to a Brownian motion? A general but often intractable answer is given by Kipnis and Varadhan. In this article we determine what conditions beyond a mean-zero condition on f(η) are required for the diffusive limit above. Specifically, we characterize the H^-1 space in an applicable way. Our method of proof relies primarily on a sharp estimate on the "spectral gap" of the process and weak regularity properties for the invariant measures.