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January 2000 Central limit theorems for additive functionals of the simple exclusion process
Sunder Sethuraman
Ann. Probab. 28(1): 277-302 (January 2000). DOI: 10.1214/aop/1019160120

Abstract

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.

Citation

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Sunder Sethuraman. "Central limit theorems for additive functionals of the simple exclusion process." Ann. Probab. 28 (1) 277 - 302, January 2000. https://doi.org/10.1214/aop/1019160120

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60017
MathSciNet: MR1756006
Digital Object Identifier: 10.1214/aop/1019160120

Subjects:
Primary: 60K35
Secondary: 60F05

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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