Universal Parametric correlations at the soft edge of the spectrum of random matrix ensembles

TL;DR

This paper extends the theory of parametric correlations in random matrix spectra to the soft edge, showing that the two-point function of level density fluctuations becomes universal after rescaling.

Contribution

It introduces a non-perturbative calculation demonstrating the universality of the two-point function at the soft edge of random matrix spectra.

Findings

Two-point function becomes universal after rescaling.

Explicit non-perturbative calculation confirms universality.

Extension of parametric correlation theory to the soft edge.

Abstract

We extend a recent theory of parametric correlations in the spectrum of random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by explicit non-perturbative calculation that the two-point function for level density fluctuations becomes, after appropriate rescaling, a universal expression.