Eigenvalue correlations for generalized Gaussian ensembles

We study the statistical properties of the eigenvalues of a generalized Gau ssian ensemble of Hermitian matrices described by a set of the variances of the matrix elements and non-invariant under an unitary transformation. We find that the eigenvalue distribution in this case can be mapped on to the corresponding distribution in Dyson's Brownian ensembles, with a function o f variances in the former playing the role of "time" in the latter. The pre -existing information about the spectral correlations of Brownian ensembles can therefore be used to obtain the same for generalized Gaussian ensemble s. (C) 2000 Elsevier Science B.V. All rights reserved.