Open Access
Translator Disclaimer
January 2003 Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes
Timo Seppäläinen, Sunder Sethuraman
Ann. Probab. 31(1): 148-169 (January 2003). DOI: 10.1214/aop/1046294307

Abstract

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density $\rho$. Place a second-class particle initially at the origin. For the case $\rho\neq 1/2$ we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functions are diffusive when $\rho\neq 1/2$. As a corollary to previous work, we deduce the invariance principle for these functionals. The main arguments are comparisons of $H_{-1}$ norms, a large deviation estimate for second-class particles and a relation between occupation times of second-class particles, and additive functional variances.

Citation

Download Citation

Timo Seppäläinen. Sunder Sethuraman. "Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes." Ann. Probab. 31 (1) 148 - 169, January 2003. https://doi.org/10.1214/aop/1046294307

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1029.60083
MathSciNet: MR1959789
Digital Object Identifier: 10.1214/aop/1046294307

Subjects:
Primary: 60K35
Secondary: 60F05

Keywords: Additive functionals , Exclusion process , invariance principle , Second-class particle

Rights: Copyright © 2003 Institute of Mathematical Statistics

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.31 • No. 1 • January 2003
Back to Top