Fluctuations and stability of fisher waves.
We have performed direct Monte Carlo simulations of the reversible diffusion-limited process {ital A}+{ital A}{leftrightarrow}{ital A} to study the effect of fluctuations on a propagating interface between stable and unstable phases. The mean-field description of this process, Fisher`s reaction-diffusion equation, admits stable nonlinear wave fronts. We find that this mean-field description breaks down in spatial dimensions 1 and 2, while it appears to be qualitatively and quantitatively accurate at and above 4 dimensions. In particular, the interface width grows {similar_to}{ital t}{sup 1/2} in 1D (exact) and {similar_to}{ital t}{sup 0.272{plus_minus}0.007} in 2D (numerical).