  For a broad class of unitary ensembles of random matrices we demonstrate the
universal nature of the Janossy densities of eigenvalues near the spectral
edge, providing a different formulation of the probability distributions of the
limiting second, third, etc. largest eigenvalues of the ensembles in question.
The approach is based on a representation of the Janossy densities in terms of
a system of orthogonal polynomials, plus the steepest descent method of Deift
and Zhou for the asymptotic analysis of the associated Riemann-Hilbert problem.
