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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-33
August 2000

Integrated density of states for random Schrödinger operators on manifolds


Norbert Peyerimhoff, Ivan Veselic


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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This paper has now been published in Geom. Dedicata 91, 117--135 (2002)