Correlation Functions of Random Matrix EnsemblesRelated to Classical Orthogonal Polynomials

In the theory of level statistics, the statistical properties of energy levels are obtained from the correlation functions of random matrix ensembles. A class of matrix ensembles, which are related to classical orthogonal polynomials, has extensively been investigated in the case of complex hermitian random matrices. We systematically evaluate the correlation functions of the random matrix ensembles in all the three cases of complex hermitian, real symmetric and self-dual quaternion random matrices.