  We study the front of the solution to the F-KPP equation with randomized
non-linearity. Under suitable assumptions on the randomness involving spatial
mixing behavior and boundedness, we show that the front of the solution lags at
most logarithmically in time behind the front of the solution of the
corresponding linearized equation, i.e. the parabolic Anderson model. This can
be interpreted as a partial generalization of Bramson's findings for the
homogeneous setting. Building on this result, we establish functional central
limit theorems for the fronts of the solutions to both equations.
