SCALING PROPERTIES OF THE EIGENVALUE SPACING DISTRIBUTION FOR BAND RANDOM MATRICES

We show that the spacing distribution for eigenvalues of band random matrices is described by a single parameter b2/N, where b is the band half-width and N is the size of the matrices. It is also shown that the eigenvalue's density obeys the semicircle law. The found scaling behaviour suggests that the fluctuation properties in the intermediate regime, between Wigner-Dyson and Poisson, are universal.