  We study the evolution of the distribution of eigenvalues of $N\times N$
matrix ensembles subject to a change of variances of its matrix elements. Our
results indicate that the evolution of the probability density is governed by a
Fokker- Planck equation similar to the one governing the time-evolution of the
particle- distribution in Wigner-Dyson gas, with relative variances now playing
the role of time. This is also similar to the Fokker-Planck equation for the
distribution of eigenvalues of a $N\times N$ matrix subject to a random
perturbation taken from the standard Gaussian ensembles with
perturbation-strength as the "time" variable. This equivalence alonwith the
already known correlations of standard Gaussian ensembles can therefore help us
to obtain the same for various physically-significant cases modeled by random
banded Gaussian ensembles.
