Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dependence of the density of states on the probability distribution for
  discrete random Schr\"odinger operators   We prove that the the density of states measure (DOSm) for random
Schr\"odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\"older-continuous in
the probability measure. The framework we develop is general enough to extend
to a wide range of discrete, random operators, including the Anderson model on
the Bethe lattice, as well as random Schr\"odinger operators on the strip. An
immediate application of our main result provides quantitive continuity
estimates for the disorder dependence of the DOSm and the integrated density of
states (IDS) in the weak disorder regime. These results hold for a general
compactly supported single-site probability measure, without any further
assumptions. The few previously available results for the disorder dependence
of the IDS valid for dimensions $d \geq 2$ assumed absolute continuity of the
single-site measure and thus excluded the Bernoulli-Anderson model. As a
further application of our main result, we establish quantitative continuity
results for the Lyapunov exponent of random Schr\"odinger operators for $d=1$
in the probability measure with respect to the weak-$^*$ topology.

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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph