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

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18 Scopus citations


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 -1/2λt0 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.

Original languageEnglish (US)
Pages (from-to)1842-1870
Number of pages29
JournalAnnals of Probability
Issue number4
StatePublished - Oct 1996


  • Central limit theorem
  • Invariance principle
  • Simple exclusion process
  • Zero-range process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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