The Furstenberg-Zimmer structure theorem for stationary random walks

TL;DR

This paper extends the Furstenberg-Zimmer structure theorem to stationary actions of locally compact second-countable groups, showing they are weakly mixing extensions of measure-preserving distal systems.

Contribution

It provides a new version of the Furstenberg-Zimmer theorem applicable to stationary actions of a broad class of groups, linking weak mixing and distal systems.

Findings

Stationary actions are weakly mixing extensions of distal systems

The theorem applies to locally compact second-countable groups

It generalizes previous results to a broader class of group actions

Abstract

We prove the following version of the Furstenberg-Zimmer structure theorem for stationary actions: Any stationary action of a locally compact second-countable group is a weakly mixing extension of a measure-preserving distal system.