Subdiffusive fluctuations of `pulled' fronts with multiplicative noise

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 Δ(t)∼t1/4, not t1/2. The subdiffusive behavior is confirmed by numerical simulations: For t<~600, these yield an effective exponent slightly larger than 1/4