FKPP fronts in quenched random media

We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity v 0 ) and deterministic disorder, quenched randomness increases the average propagation speed. We show that the velocity shift relative to the homogeneous case scales linearly with the disorder variance , with a universal prefactor —independent of the specific distribution of the disorder— such that , with . Moreover, the front position exhibits diffusive fluctuations across disorder realizations. The corresponding effective diffusion coefficient scales quadratically with , with . These results suggest a universal statistical response of FKPP fronts to quenched heterogeneity.