Densities of biased voter models on finite sets converge to Feller’s branching diffusion

J. T. Cox

Abstract: We study density processes of weakly biased voter models defined on large finite sets or graphs. Under a mixing condition on the underlying voter kernels, and for low density initial states, we prove convergence to a Feller's branching diffusion with drift. This complements results in \cite{CCC} and \cite{CC} which show convergence in the high density regime of voter model densities to the Wright\tire Fisher diffusion in the two type case, and to the Fleming\tire Viot process in the multitype case.

Journal: Markov Process. Related Fields 23, 421-444 (2017).