Journal of Theoretical Probability

, Volume 20, Issue 3, pp 505–533

Cumulants for Random Matrices as Convolutions on the Symmetric Group, II

Article

DOI: 10.1007/s10959-007-0077-y

Cite this article as:
Capitaine, M. & Casalis, M. J Theor Probab (2007) 20: 505. doi:10.1007/s10959-007-0077-y

Abstract

In a previous paper we defined some “cumulants of matrices” which naturally converge toward the free cumulants of the limiting non commutative random variables when the size of the matrices tends to infinity. Moreover these cumulants satisfied some of the characteristic properties of cumulants whenever the matrix model was invariant under unitary conjugation. In this paper we present the fitting cumulants for random matrices whose law is invariant under orthogonal conjugation. The symplectic case could be carried out in a similar way.

Keywords

CumulantsRandom matricesMatrix momentsFree probability

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.CNRS, Institut de Mathématiques de Toulouse, Equipe de Statistique et ProbabilitésUniversité Paul SabatierToulouse Cedex 09France
  2. 2.Institut de Mathématiques de Toulouse, Equipe de Statistique et ProbabilitésUniversité Paul SabatierToulouse Cedex 09France