MPS-RR 2000-33
August 2000

Integrated density of states for random Schrödinger operators on manifolds

Norbert Peyerimhoff, Ivan Veselic

Abstract

We consider a Riemannian manifold X admitting a compact quotient X/Gamma, i.e. is a cocompact subgroup of the isometries acting properly discontinuously on X. We show, under certain conditions on Gamma, that it is possible to define an integrated density of states for Gamma-ergodic random Schrödinger operators on X (see Theorem 7). These conditions are, e.g., satisfied if Gamma has polynomial growth.

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