Metric on state space of Markov chain

TL;DR

This paper explores a metric on the state space of finite irreducible Markov chains based on mean hitting times, demonstrating its properties and implications for understanding Markov chain structure.

Contribution

It establishes that the sum of mean hitting times in both directions forms a valid metric on the state space of finite irreducible Markov chains, extending previous results.

Findings

Mean hitting time satisfies the triangle inequality.

Sum of mean hitting times defines a metric on the state space.

Provides insights into the geometric structure of Markov chains.

Abstract

We consider finite irreducible Markov chains. It was shown that mean hitting time from one state to another satisfies the triangle inequality. Hence, sum of mean hitting time between couple of states in both directions is a metric on the space of states.