  We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP)
equation with a nonlocal diffusion and a stationary ergodic nonlinearity. By
employing and adapting the theory of stochastic homogenization, we show that
solutions of this equation asymptotically converge to its stationary states in
regions of space separated by a front that is determined by a Hamilton-Jacobi
variational inequality.
