Structure of trajectories of complex matrix eigenvalues in the   Hermitian-non-Hermitian transition
  The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane. 
O. Bohigas, J. X. De Carvalho and M. P. Pato
cond-mat.stat-mech math-ph math.MP