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

Under suitable analyticity conditions on the probability distribution, we s tudy the expectation of the Green function. We give precise results about d omains of holomorphic extensions in energy and exponential decay. The key i ngredient (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 se ems limited to the random Schrodinger equation, in which case however it pe rmits to treat more general probability distributions. (C) Elsevier, Paris.