We show that a sequence of voter models, suitably rescaled in space and time,converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
"Rescaled voter models converge to super-Brownian motion." Ann. Probab. 28 (1) 185 - 234, January 2000. https://doi.org/10.1214/aop/1019160117