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Wegner estimate for discrete Schrödinger operators with Gaussian random potentials

  • Martin Tautenhahn EMAIL logo
Published/Copyright: January 30, 2019

Abstract

We prove a Wegner estimate for discrete Schrödinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially; no monotonicity assumption is required. This improves earlier results where abstract conditions on the conditional distribution, compactly supported and non-negative, or compactly supported covariance functions with positive mean are considered.


Communicated by Werner Kirsch


Acknowledgements

The author gratefully acknowledges stimulating discussions with Ivan Veselić and Christoph Schumacher.

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Received: 2018-04-24
Accepted: 2018-12-20
Published Online: 2019-01-30
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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