Rescaled voter models converge to super-Brownian motion. (English) Zbl 1044.60092
Summary: 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 C. Müller and R. Tribe [Probab. Theory Relat. Fields 102, No. 4, 519–545 (1995; Zbl 0827.60050) in one dimension.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60F05 | Central limit and other weak theorems |
| 60G57 | Random measures |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
Citations:
Zbl 0827.60050References:
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