Integrated density of states for ergodic random Schr��dinger operators on manifolds

We consider the Riemannian universal covering of a compact manifold $M = X / ��$ and assume that $��$ is amenable. We show for an ergodic random family of Schr��dinger operators on $X$ the existence of a (non-random) integrated density of states.
LaTeX 2e, amsart, 17 pages; appeared in a somewhat different form in Geometriae Dedicata, 91 (1): 117-135, (2002)