Statistical Behavior of the Eigenvalues of Random Matrices

This paper will investigate the statistical behavior of the eigenvalues of real symmetric random matrices. In particular, we shall be interested in the spac-ings s between adjacent eigenvalues. Let P (s) be the distribution of these spacings, in the limit of matrices of large dimension. Empirical evidence sug-gests that, for a large class of random matrices, P (s) is given approximately by the \Wigner surmise":