Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric approach to absolutely continuous spectrum for discrete
  Schr\"odinger operators   We review a geometric approach to proving absolutely continuous (ac) spectrum
for random and deterministic Schr\"odinger operators developed in
\cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension and
present a simplified proof of ac spectrum of the Anderson model on trees. The
latter implies ac spectrum for a percolation model on trees. Finally, we
introduce certain loop tree models which lead to some interesting open
problems.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th