Recurrence and ergodicity of interacting particle systems
The authors consider the asymptotic behaviour of interacting particle systems which are not ergodic. The question arises whether a.s. the process eventually stays close to one of the ergodic states, or if it changes between the attainable ergodic states infinitely often. This behaviour is called recurrence. The authors show that under the assumption that there exists a convergence-determining class of distributions that is preserved under the dynamics, the system is recurrent. They apply their method to several interacting particle systems: the multitype voter model, interacting diffusions on \([0,1]\), interacting Fleming-Viot processes, interacting Brownian motions, mutually catalytic branching super random walks, for which they obtain recurrence results. [The erratum concerns proposition 2.3 and its proof.]
scientific article; zbMATH DE number 1439655