The existence of the integrated density of states on amenable Cayley graphs

The talk is divided into two parts: at first, we explain a general, Banach space valued, ergodic theorem for an abstract class of functions which are defined on the space of finite subsets of some countable, amenable group. Secondly, we apply the latter result to show the uniform approximation of the integrated density of states for random Schrödinger operators on metric, amenable Cayley graphs.