Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale-free uncertainty principles and Wegner estimates for random
  breather potentials   We present new scale-free quantitative unique continuation principles for
Schr\"odinger operators. They apply to linear combinations of eigenfunctions
corresponding to eigenvalues below a prescribed energy, and can be formulated
as an uncertainty principle for spectral projectors. This extends recent
results of Rojas-Molina & Veseli\'c, and Klein. We apply the scale-free unique
continuation principle to obtain a Wegner estimate for a random Schr\"odinger
operator of breather type. It holds for arbitrarily high energies.
Schr\"odinger operators with random breather potentials have a non-linear
dependence on random variables. We explain the challenges arising from this
non-linear dependence.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat