Exponential decay of averaged Green functions for random Schrodinger operators.: A direct approach

Under suitable analyticity conditions on the probability distribution, we study the expectation of the Green function. We give precise results about domains of holomorphic extensions in energy and exponential decay. The key ingredient (as in [SW]) is the construction of a probability measure in the complex domain after contour deformation. This permits us to avoid the use of perturbation series. Compared to the method in [SW], the variant here seems limited to the random Schrodinger equation, in which case however it permits to treat more general probability distributions. (C) Elsevier, Paris.