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.
"Invariant Measures for the Zero Range Process." Ann. Probab. 10 (3) 525 - 547, August, 1982. https://doi.org/10.1214/aop/1176993765