Dynamical noise sensitivity for the voter model

TL;DR

This paper investigates how the final consensus in the voter model on finite graphs responds to different types of noise, revealing stability to initial opinion perturbations but sensitivity to dynamic perturbations, using duality with coalescing random walks.

Contribution

It introduces a detailed analysis of noise sensitivity in the voter model, highlighting the contrasting effects of initial versus dynamic noise on consensus stability.

Findings

Final opinion stable under small initial perturbations

Final opinion sensitive to changes in the dynamics

Duality with coalescing random walks underpins analysis

Abstract

We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small perturbations of the initial configuration, and is sensitive to perturbations of the dynamics governing the evolution of the process. Our proofs rely on the duality relationship between the voter model and coalescing random walks, and on a precise description of this evolution when we have coupled dynamics.