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Integrated density of states for random metrics on manifolds

Lenz, D.; Peyerimhoff, N.; Veselic, I.

Authors

D. Lenz

I. Veselic



Abstract

This paper carries over the fundamental properties of random Schroedinger operators to random Laplace-Beltrami operators, that is, Laplacians with random metrics. Namely, we (A) discuss a framework for ergodic, random operators on covering manifolds with randomness entering both via potential and metrics, (B) show measurability of the introduced operators, which implies, in particular, almost sure constancy of their spectral features, (C) prove existence and the selfaveraging property of the integrated density of states together with a Pastur-Shubin type trace formula.

Citation

Lenz, D., Peyerimhoff, N., & Veselic, I. (2004). Integrated density of states for random metrics on manifolds. Proceedings of the London Mathematical Society, 88(3), 733-752. https://doi.org/10.1112/s0024611503014576

Journal Article Type Article
Online Publication Date May 1, 2004
Publication Date May 1, 2004
Deposit Date Apr 26, 2007
Journal Proceedings of the London Mathematical Society
Print ISSN 0024-6115
Electronic ISSN 1460-244X
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 88
Issue 3
Pages 733-752
DOI https://doi.org/10.1112/s0024611503014576
Keywords Integrated density of states, Random metrics, Random operators, Schrödinger operators on manifolds, Spectral density.

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