- 03-473 Ivan Veselic'
- Integrated density of states and Wegner estimates for random Schroedinger Operators
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
Proofs of the central results are given in detail. Whenever there are alternative proofs, the different approaches are compared.