Subdiffusive fluctuations of `pulled' fronts with multiplicative noise

Abstract

The stochastic wandering of pulled fronts about their mean position that is created by a local perturbation of an unstable state is studied. In the presence of multiplicative noise, pulled fronts behave subdiffusively, with Δ to approximately t1/4. This is based on two different arguments. First, the leading edge asymptotics of the relaxing pulled front is heuristically inserted into the expression for the diffusion coefficient Df of pushed fronts and Δ to approximately t1/4 is immediately obtain. The second is for the subdiffusive Δ to approximately t1/4 behavior is confirmed by numerical simulations with exponent close to 1/4.