Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-18T12:35:58.724Z Has data issue: false hasContentIssue false
  • English
  • Français

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/
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)