Level Crossing in Random Matrices: I. Random perturbation of a fixed   matrix
  We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of $\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas. 
B. Shapiro and K. Zarembo
math-ph hep-th math.MP