  For symmetric random matrices with correlated entries, which are functions of
independent random variables, we show that the asymptotic behavior of the
empirical eigenvalue distribution can be obtained by analyzing a Gaussian
matrix with the same covariance structure. This class contains both cases of
short and long range dependent random fields. The technique is based on a blend
of blocking procedure and Lindeberg's method. This method leads to a variety of
interesting asymptotic results for matrices with dependent entries, including
applications to linear processes as well as nonlinear Volterra-type processes
entries.
