Finitary isomorphisms of some infinite entropy Bernoulli flows

TL;DR

This paper constructs a finitary isomorphism between certain infinite entropy Bernoulli flows, specifically those associated with Poisson processes and Markov chains, under specific conditions, providing an elementary and explicit approach.

Contribution

It introduces an elementary, finitary construction of measure-preserving isomorphisms for infinite entropy Bernoulli flows with uniform rates and mixing properties.

Findings

Constructs explicit finitary isomorphisms

Applicable to Poisson processes and Markov chains with uniform rates

Simplifies understanding of measure-preserving systems with infinite entropy

Abstract

A consequence of Ornstein theory is that the infinite entropy flows associated with Poisson processes and continuous-time irreducible Markov chains on a finite number of states are isomorphic as measure-preserving systems. We give an elementary construction of such an isomorphism that has an additional finitariness property, subject to the additional conditions that the Markov chain has a uniform holding rate and a mixing skeleton.