We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold.
A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous
and discontinuous IDS.
Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential
and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of
a discontinuous “periodic” IDS which is regularized by a random perturbation.
Keyword and phrases integrated density of states - periodic and random operators - Schrödinger operators on manifolds - continuity properties
Mathematics Subject Classification (2000) 35J10 - 82B44
Communicated by: Kaoru Ono