Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form G(p)+V(x,omega) for a wide class of stationary ergodic random media in one space dimension. The momentum part G(p) of the Hamiltonian is a general (nonconvex) continuous function with superlinear growth at infinity, and the potential V(x,omega) is bounded and Lipschitz continuous. The class of random media we consider is defined by an explicit hill and valley condition on the diffusivity-potential pair which is fulfilled as long as the environment is not "rigid".