Weak atomic convergence of finite voter models toward Fleming-Viot processes

We consider the empirical measures of multi-type voter models with mutation on large finite sets, and prove their weak atomic convergence in the sense of Ethier and Kurtz (1994) toward a Fleming-Viot process. Convergence in the weak atomic topology is strong enough to answer a line of inquiry raised by Aldous (2013) concerning the distributions of the corresponding entropy processes and diversity processes for types.

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