We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large $t$ creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering $Delta(t) sim t^{1/4$, {em not $t^{1/2$. The subdiffusive behavior is confirmed by numerical simulations: For $tle 600$, these yield an effective exponent slightly larger than $1/4$.

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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Rocco, A., Ebert, U., & van Saarloos, W. (2000). Subdiffusive fluctuations of 'pulled' fronts with multiplicative noise. Modelling, Analysis and Simulation [MAS]. CWI.