Reaching consensus in voter model on dynamic random graphs
Rangel Baldasso (PUC-Rio)

We consider the voter model with binary opinions on a random regular graph with $n$ vertices of degree $d$, subject to a rewiring dynamics in which pairs of edges are rewired, i.e., broken into four half-edges and reconnected at random. A parameter $\nu > 0$ regulates the frequency at which the rewirings take place, in such a way that any given edge is rewired exponentially at a rate $\nu$ in the limit as $n$ grows. We show that the fraction of vertices with either one of the two opinions converges on time scale $n$ to the Fisher-Wright diffusion with an explicit diffusion constant that can be described in terms of $d$ and $\nu$. A key role in our analysis is played by the set of discordant edges, which constitutes the boundary between the sets of vertices carrying the two opinions. Based on a joint work with Luca Avena, Rajat S. Hazra, Frank den Hollander, and Matteo Quattropani.