A new proof of finitary isomorphism for Markov chains

TL;DR

This paper presents a concise and direct proof that certain countable-state mixing Markov chains with exponential return times are finitarily isomorphic to IID processes, applicable to both finite and infinite entropy cases.

Contribution

It provides a new, simplified proof of Rudolph's result on finitary isomorphism for Markov chains, extending applicability to processes with infinite entropy.

Findings

Proof works for finite and infinite entropy processes

Simplifies the understanding of Markov chain isomorphisms

Extends Rudolph's result with a more direct approach

Abstract

We give a new proof of a result of Rudolph stating that a countable-state mixing Markov chain with exponential return times is finitarily isomorphic to an IID process. Besides being short and direct, our proof has the added benefit of working for processes of finite or infinite entropy.