Markov chains through semigroup graph expansions (a survey)

TL;DR

This survey reviews recent methods of analyzing Markov chains through semigroup graph expansions, specifically the Karnofksy-Rhodes and McCammond techniques, illustrated with two examples.

Contribution

It provides a comprehensive overview of semigroup-based graph expansion methods applied to Markov chains, highlighting recent advances and practical illustrations.

Findings

Demonstrated the effectiveness of Karnofksy-Rhodes expansion in Markov chain analysis

Illustrated the application of McCammond expansion with concrete examples

Reviewed recent developments in semigroup theory applied to stochastic processes

Abstract

We review the recent approach to Markov chains using the Karnofksy-Rhodes and McCammond expansions in semigroup theory by the authors and illustrate them by two examples.