Lotka-Volterra, Voter model, Super-Brownian motion, Spatial competition, Coalescing random walk
We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
Cox, J. Theodore and Perkins, Edwin A., "Rescaled Lotka-Volterra Models Converge to Super-Brownian Motion" (2005). Mathematics Faculty Scholarship. 9.
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