Exclusion Sensitivity and Stability for the Voter Model

The notions of noise sensitivity and stability were recently extended for the voter model, a well-known and studied interactive particle system. In this model, vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend sensitivity and stability results to a different class of perturbations when the nearest neighbor exclusion process is performed in the collection of edge selections. Under the condition that the graphs have a bounded maximum degree, we prove that the consensus opinion of the voter model is “exclusion stable” when the dynamics above run for a short amount of time. This is done by analyzing the expected size of the pivotal set. Based on ongoing work with Gidi Amir, Omer Angel, and Rangel Baldasso.