Abstract
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 * n of a fixed matrix A.
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Dedicated to J. Fröhlich and T. Spencer.
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Bourgain, J. An Approach to Wegner’s Estimate Using Subharmonicity. J Stat Phys 134, 969–978 (2009). https://doi.org/10.1007/s10955-009-9729-x
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DOI: https://doi.org/10.1007/s10955-009-9729-x