  We consider two non-Gaussian ensembles of large Hermitian random matrices
with strong level confinement and show that near the soft edge of the spectrum
both scaled density of states and eigenvalue correlations follow so-called Airy
laws inherent in Gaussian unitary ensemble. This suggests that the invariant
one-matrix models should display universal eigenvalue correlations in the
soft-edge scaling limit.

Chaotic Dynamics;Statistical Mechanics;High Energy Physics - Theory;Chaotic Dynamics