Main Article
Random matrices with complex Gaussian entries

https://doi.org/10.1016/S0723-0869(03)80036-1Get rights and content
Under an Elsevier user license
open archive

Abstract

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.

Keywords

random matrices
Wigner's semi-circle law
the Marchenko-Pastur law
moment generating functions

MSC 2000 Subject Classification

15A52
46L54

Cited by (0)

1

MaPhySto — A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation.

2

Supported by the Danish Natural Science Research Council.