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

Autor:	Głuchowski, Maciej, Menz, Georg
Rok vydání:	2023
Předmět:	Mathematics - Probability 60K35 82C22
Druh dokumentu:	Working Paper
Popis:	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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.06935 Zobrazit plný text záznamu View this record from Arxiv