LEVEL SPACING FOR BAND RANDOM MATRICES

We examine the spacing distribution of the eigenvalues of tridiagonal real symmetric random matrices, the elements of which are distributed according to a Gaussian law. We show explicitly that for 4 x 4 matrices the distribution at small spacings behaves as s log2 s. We surmise that for N x N matrices the behaviour is s log(N-2) s and we present numerical results which support this conjecture.