Integrated density of states for ergodic random Schr\"odinger operators   on manifolds
  We consider the Riemannian universal covering of a compact manifold $M = X / \Gamma$ and assume that $\Gamma$ is amenable. We show for an ergodic random family of Schr\"odinger operators on $X$ the existence of a (non-random) integrated density of states. 
Norbert Peyerimhoff and Ivan Veseli\'c