Homogenization of symmetric stable-like processes in random media

We discuss homogenization problems of jump processes in random media.

We assume the media is stationary ergodic and consider the case that the (random) L\'evy density of the symmetric jump process is in average comparable to the stable process. Under some integrability condition of the L\'evy density plus some technical assumption, we establish the convergence of the resolvent to that of the stable process in the quenched sense. This is a joint work with X. Chen (Shanghai), Z.Q. Chen (Seattle) and J. Wang (Fuzhou).