Exact results and universal asymptotics in the Laguerre random matrix ensemble

Abstract

For various values of the parameters in the Laguerre random matrix ensemble, the distribution of the smallest eigenvalue and the scaled n-level distribution function are calculated exactly in terms of generalized hypergeometric functions. In certain cases these functions are expressed as multidimensional integrals, from which asymptotic formulas are calculated and predictions of universal behavior verified. © 1994 American Institute of Physics.