UNIVERSAL PARAMETRIC CORRELATIONS AT THE SOFT EDGE OF THE SPECTRUM OFRANDOM-MATRIX ENSEMBLES

We extend a recent theory of parametric correlations in the spectrum o f random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by expl icit non-perturbative calculation that, for systems with unitary symme try, the two-point function for level density fluctuations becomes, af ter appropriate rescaling, a universal expression.