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.
GA counted on the support of the Israel Science Foundation through Grant 957/20. OA is supported in part by NSERC. RB thanks the Mathematical Institute of Leiden University for support. RP was supported in part by the Israel Science Foundation Grant 2566/20.
We thank Itai Benjamini for raising the questions studied in this paper.
"Dynamical noise sensitivity for the voter model." Electron. Commun. Probab. 27 1 - 7, 2022. https://doi.org/10.1214/22-ECP483