TAYLOR AND PADE ANALYSIS OF THE LEVEL SPACING DISTRIBUTIONS OF RANDOM-MATRIX ENSEMBLES

We construct the distribution P(S) of nearest-neighbor level spacings for the orthogonal, unitary, and symplectic ensembles of (Hermitian and unitary) random matrices in the limit of large dimension. The Taylor expansion of P(S) around S=0 is given explicitly to arbitrarily high orders. By employing a diagonal Padé approximation we interpolate between the small-S behavior given by the Taylor expansion and the rigorously known asymptotic form at large S. © 1990 Springer-Verlag.