Abstract
We discuss the current state of the art in understanding consensus formation for the classical voter model on various random graph models. The voter model is a simple stochastic process in which each node in a network adopts the state of a randomly chosen neighbor at each time step, modeling opinion dynamics or information spreading. Since the ’90 it is well-understood that the time the voter model takes to achieve consensus on a given graph can be related to how a system of random walks fully coalesces. Despite this, it is still unclear in various settings how the consensus time behaves as a function of the underlying network structure and in particular of its degree distribution, except for a few stylised models. In a series of recent rigorous and non-rigorous works, we have been investigating this question in great details for various classes of random graphs clarifying possible speed up or slow-down for the consensus formation in presence of directed or undirected links, some edge-dynamics, and heavy tailed degree distributions.
Based on recent works with: Baldasso, Capannoli, Garlaschelli, Hazra, den Hollander, Quattropani.