  In this article we show the existence of limiting spectral distribution of a
symmetric random matrix whose entries come from a stationary Gaussian process
with covariances satisfying a summability condition. We provide an explicit
description of the moments of the limiting measure. We also show that in some
special cases the Gaussian assumption can be relaxed. The description of the
limiting measure can also be made via its Stieltjes transform which is
characterized as the solution of a functional equation. In two special cases,
we get a description of the limiting measure - one as a free product
convolution of two distributions, and the other one as a dilation of the Wigner
semicircular law.
