Statistical behavior of eigenvalues of real-symmetric and complex-Hermitian band matrices: Comparison with random-matrix theory

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Abstract
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.