Constanza Rojas Molina (LMU Munich)

Ergodic properties of the Delone-Anderson model

Abstract: Delone-Anderson models arise in the study of wave localization in random media, where the underlying configuration of impurities in space is aperiodic, as for example, in disordered quasicrystals. This yields a break of ergodicity, and the loss of properties linked to it. In this talk we will present recent results on the ergodic properties of such models, namely, the existence of the integrated density of states and the almost-sure spectrum. We use the framework of coloured Delone dynamical systems, which allows us to retrieve the properties known for the ergodic Anderson model, under some geometric assumptions on the underlying configuration of impurities. This is joint work with F. Germinet (U. de Cergy-Pontoise) and P. Müller (LMU Munich)