On the Stationary Measures of Two Variants of the Voter Model

Abstract In the voter model, vertices of a graph (interpreted as voters) adopt one out of two opinions (0 and 1) and update their opinions at random times by copying the opinion of a neighbor chosen uniformly at random. This process is dual to a system of coalescing random walks. The duality implies that the set of stationary measures of the voter model on a graph is linked to the dynamics of the collision of random walks on this graph. By exploring the key ideas behind this relationship, we cha