  We study the diffusion-limited reaction A + A <-> A in different spatial
dimensions to observe the effect of internal fluctuations on the interface
between stable and unstable phases. We find that, similar to what has been
observed in d=1 dimensions, internal fluctuations modify the mean-field
behavior predictions for this process, which is given by Fisher's
reaction-diffusion equation. In d > 1 the front displays local fluctuations
perpendicular to the direction of motion which, with a proper definition of the
interface, can be fully described within the Kardar-Parisi-Zhang (KPZ)
universality class. This clarifies the apparent discrepancies with KPZ
predictions reported recently.
