Daniel de la Riva

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. Furthermore, we prove heat kernel estimates for the nearest neighbor exclusion process that yield "exclusion sensitivity" when the noise runs for large enough times. Based on ongoing work with Gidi Amir, Omer Angel, and Rangel Baldasso.