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October 1996 A central limit theorem for reversible exclusion and zero-range particle systems
Sunder Sethuraman, Lin Xu
Ann. Probab. 24(4): 1842-1870 (October 1996). DOI: 10.1214/aop/1041903208

Abstract

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 $\lambda^{-1/2} \int_0^{\lambda t} f(\eta(s)) ds$ 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 $f(\eta)$ 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.

Citation

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Sunder Sethuraman. Lin Xu. "A central limit theorem for reversible exclusion and zero-range particle systems." Ann. Probab. 24 (4) 1842 - 1870, October 1996. https://doi.org/10.1214/aop/1041903208

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0872.60079
MathSciNet: MR1415231
Digital Object Identifier: 10.1214/aop/1041903208

Subjects:
Primary: 60K35
Secondary: 60F05

Keywords: central limit theorem , invariance principle , simple exclusion process , Zero-range process

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • October 1996
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