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schrödinger operators on manifolds

Proceedings of the London Mathematical Society (1)

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Integrated density of states for random metrics on manifolds
Daniel Lenz, Norbert Peyerimhoff, Ivan Veselić
Journal:

Proceedings of the London Mathematical Society / Volume 88 / Issue 3 / May 2004

Published online by Cambridge University Press:

14 April 2004, pp. 733-752

Print publication:

May 2004
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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.