Skew-orthogonal polynomials and universality of energy-level correlations - art. no. 024102

Random-matrix ensembles serve as models for quantum chaotic systems. We dev elop the theory of skew-orthogonal polynomials to study matrix ensembles wi th non-Gaussian weight functions. From the asymptotic properties of these a nd the orthogonal polynomials, we show that the local energy level correlat ions in the ensembles become universal properties independent of the global level density. This provides a rigorous justification for the universality of the Gaussian ensemble results observed in quantum chaotic systems.