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The main focus of this article is the study of ergodicity of InteractingParticle Systems (IPS). We present a simple time-scaling lemma showing thatrescaling time is equivalent to taking the convex combination of the transitionmatrix of the IPS with the identity. As a consequence, the ergodic propertiesof IPS are invariant under this transformation. Surprisingly, this almosttrivial observation has non-trivial implications. It allows us to extend anyresult that does not respect this invariance. We give three examples: First, weextend results about monotone IPS including an ergodicity criterion by Gray,and second, we extend results by Griffeath about additive and cancellative IPS.Finally, deduce a new criterion for the decay of correlation for IPS using astraightforward induction method and apply the time-scaling lemma to that aswell.

Time-Scaling, Ergodicity and Covariance Decay of Interacting Particle Systems