  In this paper, we analyze the large n-limit for random matrix with external
source with three distinct eigenvalues. And we confine ourselves in the Hermite
case and the three distinct eigenvalues are $-a,0,a$. For the case $a^2>3$, we
establish the universal behavior of local eigenvalue correlations in the limit
$n\rightarrow \infty$, which is known from unitarily invariant random matrix
models. Thus, local eigenvalue correlations are expressed in terms of the sine
kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum.
The result can be obtained by analyzing $4\times 4$ Riemann-Hilbert problem via
nonlinear steepest decent method.
