  Eigenvalue correlations of random matrix ensembles as a function of an
external perturbation are investigated vis 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.
