STATISTICAL BEHAVIOR OF EIGENVALUES OF REAL-SYMMETRICAL AND COMPLEX-HERMITIAN BAND MATRICES - COMPARISON WITH RANDOM-MATRIX THEORY

Numerical calculations have been performed with real-symmetric and complex-Hermitian matrices of dimension N having nonzero random matrix elements within a relatively narrow band of width M. It is shown that if the ratio M/N is held fixed as the matrix dimension N increases, a sequence of n eigenvalues will exhibit statistical behavior in good agreement with the predicted statistical behavior of the eigenvalues associated with the Gaussian orthogonal and the Gaussian unitary ensembles of random-matrix theory.