  We consider the spectral statistics of the superposition of a random diagonal
matrix and a GUE matrix. By means of two alternative superanalytic approaches,
the coset method and the graded eigenvalue method, we derive the two-level
correlation function $X_2(r)$ and the number variance $\Sigma^2(r)$. The graded
eigenvalue approach leads to an expression for $X_2(r)$ which is valid for all
values of the parameter $\lambda$ governing the strength of the GUE admixture
on the unfolded scale. A new twofold integration representation is found which
can be easily evaluated numerically. For $\lambda \gg 1$ the Breit-Wigner width
$\Gamma_1$ measured in units of the mean level spacing $D$ is much larger than
unity. In this limit, closed analytical expression for $X_2(r)$ and
$\Sigma^2(r)$ can be derived by (i) evaluating the double integral
perturbatively or (ii) an ab initio perturbative calculation employing the
coset method. The instructive comparison between both approaches reveals that
random fluctuations of $\Gamma_1$ manifest themselves in modifications of the
spectral statistics. The energy scale which determines the deviation of the
statistical properties from GUE behavior is given by $\sqrt{\Gamma_1}$. This is
rigorously shown and discussed in great detail. The Breit-Wigner $\Gamma_1$
width itself governs the approach to the Poisson limit for $r\to\infty$. Our
analytical findings are confirmed by numerical simulations of an ensemble of
$500\times 500$ matrices, which demonstrate the universal validity of our
results after proper unfolding.
