  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.
