1. Time-Scaling, Ergodicity and Covariance Decay of Interacting Particle Systems
- Author
-
Głuchowski, Maciej and Menz, Georg
- Subjects
Mathematics - Probability ,60K35, 82C22 - Abstract
The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the convex combination of the transition matrix of the IPS with the identity. As a consequence, the ergodic properties of IPS are invariant under this transformation. Surprisingly, this simple observation has non-trivial implications: It allows to extend any result that does not respect this invariance, which we demonstrate with examples. Additionally, we develop a recursive method to deduce decay of correlations for IPS with alphabets of arbitrary (finite) size, and apply the Time-Scaling Lemma to that as well. As an application of this new criterion we show that certain one-dimensional IPS are ergodic answering an open question of Toom et al.., Comment: 49 pages, 15 figures
- Published
- 2023