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July 2002 Stationary blocking measures for one-dimensional nonzero mean exclusion processes
Maury Bramson, Thomas Mountford
Ann. Probab. 30(3): 1082-1130 (July 2002). DOI: 10.1214/aop/1029867122

Abstract

The product Bernoulli measures $\rho_\alpha$ with densities $\alpha$, $\alpha\in [0,1]$, are the extremal translation invariant stationary measures for an exclusion process with irreducible random walk kernel $p(\cdot)$. In $d=1$, stationary measures that are not translation invariant are known to exist for specific $p(\cdot)$ satisfying $\sum_xxp(x)>0$. These measures are concentrated on configurations that are completely occupied by particles far enough to the right and are completely empty far enough to the left; that is, they are blocking measures. Here, we show stationary blocking measures exist for all exclusion processes in $d=1$, with $p(\cdot)$ having finite range and $\sum_x xp(x)>0$.

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Maury Bramson. Thomas Mountford. "Stationary blocking measures for one-dimensional nonzero mean exclusion processes." Ann. Probab. 30 (3) 1082 - 1130, July 2002. https://doi.org/10.1214/aop/1029867122

Information

Published: July 2002
First available in Project Euclid: 20 August 2002

zbMATH: 1042.60062
MathSciNet: MR1920102
Digital Object Identifier: 10.1214/aop/1029867122

Subjects:
Primary: 60K35

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 3 • July 2002
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