03-473 Ivan Veselic'

Integrated density of states and Wegner estimates for random Schroedinger Operators (1430K, PDF) Oct 22, 03

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Abstract. We survey recent results on spectral properties of random Schroedinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be applicable to random Schroedinger and Laplace-Beltrami operators on manifolds. Subsequently we study more specific models in Euclidean space, namely of alloy type, and concentrate on the regularity properties of the IDS. We discuss the role of the integrated density of states and its regularity properties for the spectral analysis of random Schroedinger operators, particularly in relation to localisation. Proofs of the central results are given in detail. Whenever there are alternative proofs, the different approaches are compared.

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