Regeneration for interacting particle systems with interactions of infinite range

Abstract

We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that the process is recurrent in the sense of Harris and construct explicit regeneration times for the process in restriction to finite cylinder sets. We show that the length of a regeneration period admits exponential moments. The proof that regeneration times are almost surely finite relies on a coupled construction of generalized house-of-cards chains.