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The Macroscopic Limit in a Stochastic Reaction-Diffusion Process

Extensive numerical simulation of a reaction-diffusion system reveals an unusual system size dependence of the fluctuation magnitude. If Ω denotes the system size parameter, e.g. particle number, fluctuations are usually predicted to be of order Ω0.5 (stable case) or Ω1 (diffusion-type case). In contrast, a scaling like Ω0.84 is observed in a combined birth-death and random walk process, which is described by a multivariate chemical master equation and corresponds to the Fisher equation in the mascoscopic limit.