## The Annals of Probability

- Ann. Probab.
- Volume 10, Number 3 (1982), 525-547.

### Invariant Measures for the Zero Range Process

#### Abstract

On a countable set of sites $S$, the zero range process is constructed when the stochastic matrix $p(x, y)$ determining the one particle motion satisfies a mild assumption. The set of invariant measures for this process is described in the following two cases: a) The system is attractive and $p(x, y)$ is recurrent. b) The system is attractive, $p(x, y)$ corresponds to a simple random walk on the integers and the rate at which particles leave any site is bounded.

#### Article information

**Source**

Ann. Probab., Volume 10, Number 3 (1982), 525-547.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993765

**Digital Object Identifier**

doi:10.1214/aop/1176993765

**Mathematical Reviews number (MathSciNet)**

MR659526

**Zentralblatt MATH identifier**

0492.60096

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Infinite particle systems invariant measures coupling

#### Citation

Andjel, Enrique Daniel. Invariant Measures for the Zero Range Process. Ann. Probab. 10 (1982), no. 3, 525--547. doi:10.1214/aop/1176993765. https://projecteuclid.org/euclid.aop/1176993765