Mixing actions of $0$-entropy for countable amenable groups

TL;DR

This paper proves that every countable infinite amenable group can act on a probability space in a way that is both mixing and has zero entropy, expanding understanding of group actions in ergodic theory.

Contribution

It introduces the existence of 0-entropy mixing actions for all countable infinite amenable groups, a novel result in ergodic theory.

Findings

Existence of 0-entropy mixing actions for all such groups

Extension of ergodic theory to broader classes of group actions

Provides new examples of mixing actions with zero entropy

Abstract

It is shown that each discrete countable infinite amenable group admits a 0-entropy mixing action on a standard probability space.