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Integrated density of states for random metrics on manifolds

Published online by Cambridge University Press:  14 April 2004

Daniel Lenz ,
Norbert Peyerimhoff  and
Ivan Veselić
Daniel Lenz
Affiliation:
Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany. E-mail: dlenz@mathematik.tu-chemnitz.de, www.tu-chemnitz.de/mathematik/analysis/dlenz
Norbert Peyerimhoff
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany. E-mail: peyerim@math.ruhr-uni-bochum.de, www.ruhr-uni-bochum.de/mathematik10/Norbert.html
Ivan Veselić
Affiliation:
Forschungsstipendiat der Deutschen Forschungsgemeinschaft Current address: Forschungsstipendiat der Deutschen Forschungsgemeinschaft. Current address: Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA. E-mail: ivan.veselic@ruhr-uni-bochum.de, http://homepage.ruhr-uni-bochum.de/Ivan.Veselic/
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Abstract

We study ergodic random Schrödinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties, the existence of a self-averaging integrated density of states and a Pastur–šubin type trace formula.

Keywords

integrated density of statesrandom metricsrandom operatorsSchrödinger operators on manifoldsspectral density35J1058J3582B44
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 88 , Issue 3 , May 2004 , pp. 733 - 752
Copyright
2004 London Mathematical Society

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