Delone dynamical systems and associated random operators

Abstract

We carry out a careful study of basic topological and ergodic features of Delone dynamical systems. We then investigate the associated topological groupoids and in particular their representations on certain direct integrals with non constant fibres. Via non-commutative-integration theory these representations give rise to von Neumann algebras of random operators. Features of these algebras and operators are discussed. Restricting our attention to a certain subalgebra of tight binding operators, we then discuss a Shubin trace formula.

19 pages; revised version

References in corpus (3)

• Non Commutative Geometry of Tilings and Gap Labelling
• Pure Point Dynamical and Diffraction Spectra
• The Local Structure of Tilings and their Integer Group of Coinvariants

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