The Annals of Probability

Stationary blocking measures for one-dimensional nonzero mean exclusion processes

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 $\sum_x xp(x)>0$.

Article information

Source
Ann. Probab., Volume 30, Number 3 (2002), 1082-1130.

Dates
First available in Project Euclid: 20 August 2002

https://projecteuclid.org/euclid.aop/1029867122

Digital Object Identifier
doi:10.1214/aop/1029867122

Mathematical Reviews number (MathSciNet)
MR1920102

Zentralblatt MATH identifier
1042.60062

Citation

Bramson, Maury; Mountford, Thomas. Stationary blocking measures for one-dimensional nonzero mean exclusion processes. Ann. Probab. 30 (2002), no. 3, 1082--1130. doi:10.1214/aop/1029867122. https://projecteuclid.org/euclid.aop/1029867122

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• MINNEAPOLIS, MINNESOTA 55455 E-MAIL: bramson@math.umn.edu DÉPARTEMENT DE MATHÉMATIQUES ÉCOLE POLy TECHNIQUE FÉDÉRALE DE LAUSANNE ECUBLENS CH 1015 SWITZERLAND E-MAIL: thomas.mountford@epfl.ch