Abstract
We study the front of the solution to the F-KPP equation with randomized non-linearity. Under suitable assumptions on the randomness including 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 (Bramson in Commun Pure Appl Math 31(5):531–581, 1978) for the homogeneous setting. Partially building on this result and its derivation, we establish functional central limit theorems for the fronts of the solutions to both equations.
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