  It is shown how the universal correlation function of Brezin and Zee, and
Beenakker, for random matrix ensembles of Wigner-Dyson type with density
support on a finite interval can be derived using a linear response argument
and macroscopic electrostatics. The analogous formula for ensembles of unitary
random matrices is derived using the same method, and the corresponding global
fluctuation formula for the variance of a linear statistic is presented. The
result for the universal correlation is checked using an exact result for the
finite system two-point correlation in the Dyson circular ensemble at all even
$\beta$.
