98-81 J. Sj\"ostrand, W.-M. Wang

Exponential decay of averaged Green functions for random Schr\"odinger operators, a direct approach (47K, TEX) Feb 24, 98

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Abstract. 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 our paper [SW] Supersymmetric measures and Maximum principle in the complex domain : exponential decay of the Green's function) 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 Schr\"odinger equation, in which case however it permits to treat more general probability distributions

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