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Integrated density of states for random metrics on manifolds

Lenz, Daniel and Peyerimhoff, Norbert and Veselic, Ivan (2004) Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society, 88 (3). pp. 733-752. ISSN 0024-6115. doi:10.1112/S0024611503014576.

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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.

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Lenz, Daniel0000-0001-5820-475X
Additional Information:Copyright © 2004 London Mathematical Society. Received September 17 2002. Published online by Cambridge University Press 14 April 2004. It is a pleasure to thank B. Franke, D. Hundertmark, L. Karp, W. Kirsch, O. Post and P. Stollmann for stimulating discussions. This work was supported in part by the DFG through SFB 237 ‘Unordnung und groVe Fluktuationen’ and the Schwerpunktprogramm ‘Interagierende stochastische Systeme von hoher Komplexitat’. I. Veselic thanks B. Simon for hospitality at CalTech.
Subject Keywords:integrated density of states; random metrics; random operators; Schrödinger operators on manifolds; spectral density
Issue or Number:3
Record Number:CaltechAUTHORS:LENplms04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5055
Deposited By: Tony Diaz
Deposited On:25 Sep 2006
Last Modified:08 Nov 2021 20:22

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