Ergodic Theorem for nonstationary random walks on compact abelian groups

TL;DR

This paper proves an ergodic theorem for nonstationary random walks on compact abelian groups, showing convergence to Haar measure and establishing large deviation estimates under classical assumptions.

Contribution

It extends ergodic theory to nonstationary settings on compact abelian groups, providing new convergence and deviation results.

Findings

Weak-* convergence to Haar measure

Ergodic Theorem established

Large deviation estimates proved

Abstract

We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.