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 $\mathrm{\Delta }(t)\sim t^{1\mathrm{/}4}$, {\em not} $t^{1\mathrm{/}2}$. The subdiffusive behavior is confirmed by numerical simulations: For $t\le 600$, these yield an effective exponent slightly larger than 1/4.