Asymptotically Exactly Solvable Models of Processes in Stochastically Homogeneous Disordered Lattice Media

We construct and study asymptotically exactly solvable models (including new models) of evolution processes in random stationary stochastically homogeneous lattice media. For the first time, we present an effective method for obtaining long-time asymptotic expansions for spatial fluctuations of the propagator in many models previously studied as well as in new models.