Abstract
Eigenvalue correlations of random matrix ensembles as a function of an external (parametric) perturbation are investigated via the Dyson Brownian-motion model in the situation where the level density has a hard edge singularity. By solving a linearized hydrodynamical equation, a universal dependence of the density-density correlator on the external field is found. As an application, we obtain a formula for the variance of linear statistics with the parametric dependence exhibited as a Laplace transform.
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