The Annals of Probability

Central limit theorems for additive functionals of the simple exclusion process

Sunder Sethuraman

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Some invariance principles for additive functionals of simple exclusion with finite-range translation-invariant jump rates $p(i, j) = p(j - i)$ in dimensions $d \geq1$ are established. A previous investigation concentrated on the case of $p$ symmetric. The principal tools to take care of nonreversibility, when $p$ is asymmetric, are invariance principles for associated random variables and a “local balance”estimate on the asymmetric generator of the process.

As a by-product,we provide upper and lower bounds on some transition probabilities for mean-zero asymmetric second-class particles,which are not Markovian, that show they behave like their symmetric Markovian counterparts.Also some estimates with respect to second-class particles with drift are discussed.

In addition,a dichotomy between the occupation time process limits in $d =1$ and $d \geq 2$ for symmetric exclusion is shown. In the former, the limit is fractional Brownian motion with parameter 3/4, and in the latter, the usual Brownian motion.

Article information

Ann. Probab., Volume 28, Number 1 (2000), 277-302.

First available in Project Euclid: 18 April 2002

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F05: Central limit and other weak theorems

Invariance principle central limit theorem simple exclusion process FKG associated second-class particles


Sethuraman, Sunder. Central limit theorems for additive functionals of the simple exclusion process. Ann. Probab. 28 (2000), no. 1, 277--302. doi:10.1214/aop/1019160120.

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