## The Annals of Probability

### Coupling the Simple Exclusion Process

Thomas M. Liggett

#### Abstract

Consider the infinite particle system on the countable set $S$ with the simple exclusion interaction and one-particle motion determined by the stochastic transition matrix $p(x, y)$. In the past, the ergodic theory of this process has been treated successfully only when $p(x, y)$ is symmetric, in which case great simplifications occur. In this paper, coupling techniques are used to give a complete description of the set of invariant measures for the system in the following three cases: (a) $p(x, y)$ is translation invariant on the integers and has mean zero, (b) $p(x, y)$ corresponds to a birth and death chain on the nonnegative integers, and (c) $p(x, y)$ corresponds to the asymmetric simple random walk on the integers.

#### Article information

Source
Ann. Probab. Volume 4, Number 3 (1976), 339-356.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996084

Digital Object Identifier
doi:10.1214/aop/1176996084

Mathematical Reviews number (MathSciNet)
MR418291

Zentralblatt MATH identifier
0339.60091

JSTOR

#### Citation

Liggett, Thomas M. Coupling the Simple Exclusion Process. Ann. Probab. 4 (1976), no. 3, 339--356. doi:10.1214/aop/1176996084. https://projecteuclid.org/euclid.aop/1176996084.