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

• 成果类型: Article
• 署名作者: Sethuraman, S; Xu, L
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 1842-1870
• 关键词: diffusion

摘要

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 eta(t) be the configuration of the process at time t and let f(eta) be a function on the state space. The question is: For which functions f does lambda(-1/2)integral(0)(M) f(eta(s)) ds converge to a Brownian motion? A general but often intractable answer is given by Kipnis and Varadhan. In this article Re determine what conditions beyond a mean-zero condition on f(eta) 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.