Parametric level statistics in random matrix theory: Exact solution

An exact solution to the problem of parametric level statistics in non-Gaus sian ensembles of N x N Hermitian random matrices with either soft or stron g level confinement is formulated within the framework of the orthogonal po lynomial technique. Being applied to random matrices with strong level conf inement, the solution obtained leads to emergence of a new connection relat ion that makes a link between the parametric level statistics and the scala r two-point kernel in the thermodynamic limit. [S0031-9007(99)08876-6].