Central Limit Theorem for Zero-Range Processes

Abstract

We consider additive functionals INTt-0 V(ns )ds of symmetric zero-range processes, where V is a mean zero local function. In dimensions 1 and 2 we obtain a central limit theorem for a-1(t) INTt-0 V(ns)ds with a(t) = SQRROOT (tlogt) in d =2 and a(t) = t 3/4 in d = 1 and an explicit form for the asymptotic variance SIGMA2. The transient case d greater than or equal to 3 can be handled by standard arguments [KV, SX,S]. We also obtain corresponding invariance principles. This generalizes results obtained by Port (see [CG]) for noninteracting random walks and Kipnis [K] for the symmetric simple exclusion process. Our main tools are the martingale method together with L2 decay estimates [JLQY] for the process semigroup.