Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older regularity of the integrated density of states for
  quasi-periodic long-range operators on $\ell^2(\Z^d)$   We prove the H\"older continuity of the integrated density of states for a
class of quasi-periodic long-range operators on $\ell^2(\Z^d)$ with large
trigonometric polynomial potentials and Diophantine frequencies. Moreover, we
give the H\"older exponent in terms of the cardinality of the level sets of the
potentials, which improves, in the perturbative regime, the result obtained by
Goldstein and Schlag \cite{gs2}. Our approach is a combination of Aubry
duality, generalized Thouless formula and the regularity of the Lyapunov
exponents of analytic quasi-periodic $GL(m,\C)$ cocycles which is proved by
quantitative almost reducibility method.

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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin