Integrated density of states for ergodic random Schrödinger operators on manifolds

Abstract

We consider the Riemannian universal covering of a compact manifold $M = X / Γ$ and assume that $Γ$ is amenable. We show for an ergodic random family of Schrödinger 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)