Dynamical noise sensitivity for the voter model

We study how the consensus opinion of the voter model on finite graphs varies in light of noise sensitivity with respect to both the initial opinions and the dynamics. We first prove that the final opinion is stable with respect to small perturbations of the initial configuration. Different effects are observed when a perturbation is introduced in the dynamics governing the evolution of the process, and the final opinion is noise sensitive in this case. Our proofs rely on the relationship between the voter model and coalescing random walks, and on a precise description of this evolution when we have coupled dynamics.