The Evolving Voter Model on Thick Graphs
Anirban Basak, Rick Durrett, and Yuan Zhang
Abstract. In the evolving voter model, when an individual interacts with a neighbor having an opinion different from theirs, they will with probability 1-&alpha: imitate the neighbor but with probability α will sever the
connection and choose a new neighbor at random (i) from the graph or (ii) from those with the same opinion. Durrett et al. (2012) used simulation and heuristics to study these dynamics on sparse graphs. Recently Basu and Sly (2016) have analyzed this system with 1-α = ν/N on a dense Erdos-Renyi graph G(N,1/2) and
rigorously proved that there is a phase transition from rapid disconnection into components with a single opinion
to prolonged persistence of discordant edges as $\nu$ increases. In this paper, we consider the intermediate situation of Erdos-Renyi random graphs with average degree L=Na where 0 < a < 1. Most of the paper is devoted to a rigorous analysis of an approximation of the dynamics called the approximate master equation.
Using ideas of Lawley, Mattingly, and Reed (2014) and Silk (2014) we are able to analyze these dynamics in great detail.
Preprint
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