Self-consistent perturbation theory for random matrix ensembles

An arbitrary but known random matrix ensemble is subjected to a perturbation by any of the three classical random matrix ensembles (GOE, GUE and GSE). Using a BBGKY hierarchy for the correlation functions of the eigenvalues, they propose a self-consistent perturbation expansion and give the result for the two-point function to lowest order in integral form. By way of illustration, the integral is solved for the special case of a Poisson ensemble perturbed by any of the classical ensembles, thereby recovering a result previously derived by other methods.