Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity theorem of singular Spectrum for general Anderson type
  Hamiltonian   In this work, we focus on the multiplicity of singular spectrum for operators
of the form $A^\omega=A+\sum_{n}\omega_n C_n$ on a separable Hilbert space
$\mathcal{H}$, for a self-adjoint operator $A$ and a countable collection
$\{C_n\}_{n}$ of non-negative finite rank operators. When $\{\omega_n\}_n$ are
independent real random variables with absolutely continuous distributions, we
show that the multiplicity of singular spectrum is almost surely bounded above
by the maximum algebraic multiplicity of eigenvalues of
$\sqrt{C_n}(A^\omega-z)^{-1}\sqrt{C_n}$ for all $n$ and almost all
$(z,\omega)$. The result is optimal in the sense that there are operators where
the bound is achieved. Using this, we also provide effective bounds on
multiplicity of singular spectrum for some special cases.

23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys