  We consider $n\times n$ real symmetric and hermitian random matrices
$H_{n,m}$ equals the sum of a non-random matrix $H_{n}^{(0)}$ matrix and the
sum of $m$ rank-one matrices determined by $m$ i.i.d. isotropic random vectors
with log-concave probability law and i.i.d. random amplitudes $\{\tau_{\alpha
}\}_{\alpha =1}^{m}$. This is a generalization of the case of vectors uniformly
distributed over the unit sphere, studied in [Marchenko-Pastur (1967)]. We
prove that if $n\to \infty, m\to \infty, m/n\to c\in \lbrack 0,\infty)$ and
that the empirical eigenvalue measure of $H_{n}^{(0)}$ converges weakly, then
the empirical eigenvalue measure of $H_{n,m}$ converges in probability to a
non-random limit, found in [Marchenko-Pastur (1967)].
