Integrated density of states for ergodic random Schrödinger operators on manifolds

Abstract

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 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)

Cited by in corpus (5)

• Spectral Analysis of Percolation Hamiltonians
• Quantum site percolation on amenable graphs
• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states
• Continuity of the integrated density of states on random length metric graphs
• Continuity properties of the integrated density of states on manifolds