A note on a local ergodic theorem for an infinite tower of coverings

TL;DR

This paper discusses a local ergodic theorem for a symmetric exclusion process on an infinite tower of coverings linked to a specific class of groups, expanding understanding of ergodic behavior in complex structures.

Contribution

It introduces a local ergodic theorem for symmetric exclusion processes on infinite towers of coverings associated with residually finite amenable groups, a novel extension in ergodic theory.

Findings

Establishes a local ergodic theorem for the process

Connects ergodic properties with group-theoretic structures

Provides a framework for analyzing similar processes on complex coverings

Abstract

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.