Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An introduction to multiscale techniques in the theory of Anderson
  localization. Part I   These lectures present some basic ideas and techniques in the spectral
analysis of lattice Schrodinger operators with disordered potentials. In
contrast to the classical Anderson tight binding model, the randomness is also
allowed to possess only finitely many degrees of freedom. This refers to
dynamically defined potentials, i.e., those given by evaluating a function
along an orbit of some ergodic transformation (or of several commuting such
transformations on higher-dimensional lattices). Classical localization
theorems by Frohlich--Spencer for large disorders are presented, both for
random potentials in all dimensions, as well as even quasi-periodic ones on the
line. After providing the needed background on subharmonic functions, we then
discuss the Bourgain-Goldstein theorem on localization for quasiperiodic
Schrodinger cocycles assuming positive Lyapunov exponents.

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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an