  Random matrices whose entries come from a stationary Gaussian process are
studied. The limiting behavior of the eigenvalues as the size of the matrix
goes to infinity is the main subject of interest in this work. It is shown that
the limiting spectral distribution is determined by the absolutely continuous
component of the spectral measure of the stationary process, a phenomenon
resembling that in the situation where the entries of the matrix are i.i.d. On
the other hand, the discrete component contributes to the limiting behavior of
the eigenvalues in a completely different way. Therefore, this helps to define
a boundary between short and long range dependence of a stationary Gaussian
process in the context of random matrices.
