Fluid Limit of Threshold Voter Models on Tori

In this paper, we are concerned with threshold voter models on tori. Assuming that the initial distribution of the process is product measure with density p, we obtain a fluid limit of the proportion of vertices in state 1 as the dimension of the torus grows to infinity. The fluid limit performs a phase transition phenomenon from p < 1/2 to p > 1/2.
18 pages