Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multiplicity of spectrum for Anderson type operators with higher rank
  perturbations   Here, we focus on Anderson type operators over infinite graphs where the
randomness acts through higher rank perturbations. We show that for special
family of graphs, the operator has non-trivial multiplicity for its pure point
spectrum. We, also, show that for some family of graphs, any unitary which
fixes the random operator, arising from an automorphism of the graph is
identity; but that, for these graphs the spectrum of the random operator has
non-trivial multiplicity.

36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat