  We are going to study the limiting spectral measure of fixed dimensional
Hermitian block-matrices with large dimensional Wigner blocks. We are going
also to identify the limiting spectral measure when the Hermitian
block-structure is Circulant. Using the limiting spectral measure of a
Hermitian Circulant block-matrix we will show that the spectral measure of a
Wigner matrix with $k-$weakly dependent entries need not to be the semicircle
law in the limit.
