Eigenvalue correlations for banded matrices

We study the evolution of the distribution of eigenvalues of a N x N matrix ensemble subject to a change of the distribution parameters of its matrix elements. Our results indicate that the evolution of the probability densit y is governed by a Fokker-Planck equation similar to the one governing the time evolution of the particle distribution in Wigner-Dyson gas, with a fun ction of distribution parameters now playing the role of time. This equival ence alongwith the already known particle density correlations of Wigner-Dy son gas can therefore help us to obtain the eigenvalue correlations for var ious physically significant cases modeled by random banded and sparse Gauss ian ensembles. (C) 2001 Elsevier Science B.V. All rights reserved.