An Ergodic Theorem for Delone Dynamical Systems and Existence of the Integrated Density of States

We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we prove existence of the integrated density of states in the sense of uniform convergence in distribution for the associated random operators. Dedicated to J. Voigt on the occasion of his 60th birthday 1 Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany; E-mail: [email protected], 2 Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany; E-mail: [email protected]