Recurrence and ergodicity of interacting particle systems

Many interacting particle systems with short range interactions are not erg odic, but converge weakly towards a mixture of their ergodic invariant meas ures. The question arises whether a.s. the process eventually stays close t o one of these ergodic states, or if it changes between the attainable ergo dic states infinitely often ("recurrence"). Under the assumption that there exists a convergence-determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a mode l of mutually catalytic branching.