Random Schrodinger Operators on Manifolds,

#### D. Lenz, N. Peyerimhoff, I. Veselic

2003, v.9, №4, 717-728

ABSTRACT

We consider a random family of Schrodinger operators on a cover $X$ of a compact Riemannian manifold $M = X/\Gamma$. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and existence and non-randomness of an integrated density of states. We also sketch a groupoid based general framework which allows to treat basic features of random operators in different contexts in a unified way. Further topics of research are also discussed.

Keywords: integrated density of states,random metrics,random operators,Schrodinger operators on manifolds,Von Neumann algebra,trace