Discontinuities of the Integrated Density of States for Random Operators on Delone Sets

Despite all the analogies with usual random models, tight binding operators for quasicrystals exhibit a feature that clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is identified as a local effect, due to the occurrence of eigenfunctions with bounded support.Research partly supported by the DFG in the priority program Quasicrystals