Supersymmetric measures and maximum principles in the complex domain. Exponential decay of Green's functions

We study a class of holomorphic complex measures which are, in an appropria te sense, close to a complex Gaussian. We show that these measures can be r educed to a product measure of real Gaussians with the aid of a maximum pri nciple in the complex domain. The formulation of this problem has its origi n in the study of a certain class of random Schrodinger operators, for whic h we show that the expectation value of the Green's function decays exponen tially. (C) Elsevier, Paris.