Regeneration for interacting particle systems with interactions of infinite range

TL;DR

This paper studies an infinite-range interacting particle system on a lattice, establishing recurrence, constructing explicit regeneration times, and proving exponential moment bounds for these regeneration periods.

Contribution

It introduces a method to construct explicit regeneration times for infinite-range interactions under high-noise conditions, extending previous finite-range results.

Findings

Process is recurrent under specified conditions

Explicit regeneration times are constructed

Regeneration periods have exponential moments

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.