Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level curvature distribution: from bulk to the soft edge of random
  Hermitian matrices   Level curvature is a measure of sensitivity of energy levels of a
disordered/chaotic system to perturbations. In the bulk of the spectrum Random
Matrix Theory predicts the probability distributions of level curvatures to be
given by Zakrzewski-Delande expressions [F. von Oppen {\it Phys. Rev. Lett.}
{\bf 73} 798 (1994) & {\it Phys.Rev. E} {\bf 51} 2647 (1995); Y.V. Fyodorov and
H.-J. Sommers {\it Z.Phys.B} {\bf 99} 123 (1995)]. Motivated by growing
interest in statistics of extreme (maximal or minimal) eigenvalues of
disordered systems of various nature, it is natural to ask about the associated
level curvatures. I show how calculating the distribution for the curvatures of
extreme eigenvalues in GUE ensemble can be reduced to studying asymptotic
behaviour of orthogonal polynomials appearing in the recent work C. Nadal and
S. N. Majumdar {\it J. Stat. Mech.} {\bf 2011} P04001 (2011). The corresponding
asymptotic analysis being yet outstanding, I instead will discuss solution of a
related, but somewhat simpler problem of calculating the level curvature
distribution averaged over all the levels in a spectral window close to the
edge of the semicircle. The method is based on asymptotic analysis of kernels
associated with Hermite polynomials and their Cauchy transforms, and is
straightforwardly extendable to any rotationally-invariant ensemble of random
matrices.

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg