Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level statistics of one-dimensional Schr\"odinger operators with random
  decaying potential   We study the level statistics of one-dimensional Schr\"odinger operator with
random potential decaying like $x^{-\alpha}$ at infinity. We consider the point
process $\xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac
spectrum case) for $\alpha > \frac 12$, $\xi_L$ converges to a clock process,
and the fluctuation of the eigenvalue spacing converges to Gaussian.
(ii)(critical case) for $\alpha = \frac 12$, $\xi_L$ converges to the limit of
the circular $\beta$-ensemble.

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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph