J. Sj\"ostrand, W.-M. Wang
Exponential decay of averaged Green functions for
random Schr\"odinger operators, a direct approach 
(47K, TEX)

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