Subdiffusive fluctuations of "pulled" fronts with multiplicative noise

We study the propagation of a ''pulled'' front with multiplicative noise th at is created by a local perturbation of an unstable state. Unlike a front propagating into a metastabre state, where a separation of time scales for sufficiently target creates a diffusive wandering of the front position abo ut its mean, we predict that for so-caned pulled fronts, the fluctuations a re subdiffusive with root mean square wandering Delta(t)similar to t(1/4), not t(1/2). The subdiffusive behavior is confirmed by numerical simulations : For t less than or equal to 600, these yield an effective exponent slight ly larger than 1/4.