Dynamical noise sensitivity for the voter model

Electronic Communications in Probability, vol. 27

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.

Authors 4

1. Gideon Amir

   Bar-Ilan University

   Affiliation as printed

   Department of Mathematics, Bar-Ilan University

2. Omer Angel

   University of British Columbia

   Affiliation as printed

   Department of Mathematics, University of British Columbia

3. Rangel Baldasso Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University

4. Ron Peretz

   Bar-Ilan University

   Affiliation as printed

   Economics Department, Bar-Ilan University