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Groupoids, von Neumann algebras and the integrated density of states

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


D. Lenz

I. Veselic


We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define an abstract density of states. While the treatment applies to a general framework we lay special emphasis on three particular examples: random Schroedinger operators on manifolds, quantum percolation and quasi crystal Hamiltonians. For these examples we show that the distribution function of the abstract density of states coincides with the integrated density of states defined via an exhaustion procedure.


Lenz, D., Veselic, I., & Peyerimhoff, N. (2007). Groupoids, von Neumann algebras and the integrated density of states. Mathematical Physics, Analysis and Geometry, 10(1), 1-41.

Journal Article Type Article
Acceptance Date Mar 12, 2007
Online Publication Date May 17, 2007
Publication Date 2007-02
Journal Mathematical Physics, Analysis and Geometry
Print ISSN 1385-0172
Electronic ISSN 1572-9656
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 10
Issue 1
Pages 1-41
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