Random matrices with complex Gaussian entries

In this paper we give new and purely analytical proofs of a number of classical results on the asymptotic behavior of large random matrices of complex Wigner type (the GUE-case) or of complex Wishart type: Wigner's semi-circle law, the Harer-Zagier recursion formula, the Marchenko-Pastur law, the Geman-Silverstein results on the largest and smallest eigenvalues and other related results. Our approach is based on the derivation of explicit formulae for the moment generating functions for random matrices of the two considered types.