Universal Behavior of Correlations between Eigenvalues of Random   Matrices
  The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare correlation of the eigenvalues are not universal, the connected correlation shows a universal behavior after smoothing. 
T. S. Kobayakawa, Y. Hatsugai, M. Kohmoto and A. Zee