Unitary random-matrix ensemble with governable level confinement

A family of unitary {α} ensembles of random matrices with governable confinement potential V(x){~}{}x^α is studied employing exact results of the theory of nonclassical orthogonal polynomials. The density of levels, two-point kernel, locally rescaled two-level cluster function, and smoothed connected correlations between the density of eigenvalues are calculated for strong ({α}>1) and border ({α}=1) level confinement. It is shown that the density of states is a smooth function for {α}>1, and has a well-pronounced peak at the band center for {α}{≤}1. The case of border level confinement associated with transition point {α}=1 is reduced to the exactly solvable Pollaczek random-matrix ensemble. Unlike the density of states, all the two-point correlators remain (after proper rescaling) universal down to and including {α}=1. {} 1996 The American Physical Society.