Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrated density of states and Wegner estimates for random
  Schr\"odinger Operators   We survey recent results on spectral properties of random Schr\"odinger
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 Schr\"odinger 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 Schr\"odinger 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.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
18
The categories of this paper are: econ
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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th