Information flow in discrete Markov systems

Abstract

Infinite systems of interacting Markov chains are investigated. Some basic concepts of the ergodic theory of such systems are first presented. In particular, the question of the uniqueness and multiplicity of invariant probability measures is considered. In the case of one-dimensional systems, the question is studied in detail by investigating the flow of information throughout the system and some criteria for the uniqueness of invariant probability measures are obtained.