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 Ohm denotes the system size parameter, e.g. particle number, fluctuations are usually predicted to be of order Ohm(0.5) (stable case) or Ohm(1) (diffusion-type case). In contrast, a scaling like Ohm(0.84) 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.