An Approach to Wegner’s Estimate Using Subharmonicity

We develop a strategy to establish a Wegner estimate and localization in random lattice Schrödinger operators on $\Bbb{Z}^{d}$ , which does not rely on the usual eigenvalue variation argument. Our assumption is that the potential V(ω) depends real analytically on ω and we use a distributional property of analytic functions in many variables. An application is given to models where V n is a self-adjoint matrix obtained by random unitary conjugation V n =U n AU * of a fixed matrix A.