Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on spectral averaging and the local density of states for
  random Schr\"odinger operators on $L^2 ( R^d )$   We prove some local estimates on the trace of spectral projectors for random
Schr\"odinger operators restricted to cubes $\Lambda \subset R^d$. We also
present a new proof of the spectral averaging result based on analytic
perturbation theory. Together, these provide another proof of the Wegner
estimate with an explicit form of the constant and an alternate proof of the
Birman-Solomyak formula. We also use these results to prove the Lipschitz
continuity of the local density of states function for a restricted family of
random Schr\"odinger operators on cubes $\Lambda \subset R^d$, for $d \geq 1$.
The result holds for low energies without a localization assumption but is not
strong enough to extend to the infinite-volume limit.

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol