We study the averaging problem for a divergence form random parabolic operators with a large potential and with coefficients rapidly oscillating both in space and time variables. We assume that the medium possesses the periodic microscopic structure while the dynamics of the system is random...

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization,...