Ensemble average of an arbitrary number of pairs of different eigenvalues using Grassmann integration (Q1081946)

An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average of S different pairs of eigenvalues of a GOE is given by \((-1)^ S2^{-S}\pi^{-1/2}\Gamma (S+)\).