Non-ergodicity for the noisy majority vote process on trees

TL;DR

This paper proves the existence of multiple equilibrium measures in the noisy majority vote process on infinite regular trees with degree at least 3, demonstrating non-ergodicity and extending previous results for higher degrees.

Contribution

It extends the understanding of non-ergodicity in noisy majority vote processes to trees with degree 3 and above, broadening prior work limited to degree 5 and higher.

Findings

Existence of multiple equilibrium measures for degree d≥3

Non-ergodicity demonstrated in the noisy majority vote process

Extension of previous results from degree 5 to degree 3 and above

Abstract

We consider the noisy majority vote process on infinite regular trees with degree $d\geq 3$, and we prove the non-ergodicity, i.e., there exist multiple equilibrium measures. Our work extends a result of Bramson and Gray (2021) for $d\geq 5$.