Presentation of many new results in one place for the first time.
First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals.
Fredholm determinants and Painlevé equations.
The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.
Fredholm determinants and inverse scattering theory.
Probability densities of random determinants.