Random walk in a finite directed graph subject to a synchronizing road coloring

TL;DR

This paper proves that any ergodic Markov chain can be represented as a random walk on a finite directed graph with a synchronizing road coloring, and analyzes the redundancy in such realizations.

Contribution

It provides a constructive proof for representing ergodic Markov chains as synchronized random walks and studies the redundancy involved.

Findings

Any ergodic Markov chain can be realized as a synchronized random walk.

Redundancy (extra entropy) in such realizations is quantifiable.

The paper offers a constructive method for this realization.

Abstract

A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.