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January 2004 Fluctuations in the occupation time of a site in the asymmetric simple exclusion process
Cédric Bernardin
Ann. Probab. 32(1B): 855-879 (January 2004). DOI: 10.1214/aop/1079021466

Abstract

We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density $\rho$. We prove that for dimension $d=2$ the occupation time of the site 0 is diffusive as soon as $\rho\neq 1/2$. For dimension $d=1$, if the density $\rho$ is equal to $1/2$, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as $t^{5/4}$.

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Cédric Bernardin. "Fluctuations in the occupation time of a site in the asymmetric simple exclusion process." Ann. Probab. 32 (1B) 855 - 879, January 2004. https://doi.org/10.1214/aop/1079021466

Information

Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1071.60096
MathSciNet: MR2039945
Digital Object Identifier: 10.1214/aop/1079021466

Subjects:
Primary: 60K35
Secondary: 60F05

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1B • January 2004
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