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

TL;DR

This paper proves that empirical measures of multi-type voter models with mutation on large finite sets converge weakly to Fleming-Viot processes, providing insights into entropy and diversity distributions.

Contribution

It establishes weak atomic convergence of voter models to Fleming-Viot processes, addressing open questions about entropy and diversity distributions.

Findings

Empirical measures converge weakly to Fleming-Viot processes.

Convergence results apply to entropy and diversity processes.

Addresses questions raised by Aldous (2013).

Abstract

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.