Densities of Biased Voter Models on Finite Sets Converge to Feller's Branching Diffusion

#### J.T. Cox

2017, v.23, Issue 3, 421-444

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.

Keywords: biased voter model, coalescing Markov chains, Feller's branching diffusion, mixing times