Interacting two-state Markov chains on undirected networks

TL;DR

This paper proves that two-state Markov chains interacting bilinearly on undirected networks have a unique stable steady state, using an elementary proof based on the relative entropy function.

Contribution

It introduces a simple proof demonstrating the existence and uniqueness of the stable steady state for interacting two-state Markov chains on networks.

Findings

Existence of a unique stable steady state

Elementary proof using relative entropy

Applicable to bilinear interactions on undirected networks

Abstract

It is shown that irreducible two-state continuous-time Markov chains interacting on a network in a bilinear fashion have a unique stable steady state. The proof is elementary and uses the relative entropy function.