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

Author

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  • M. Capitaine

    (Université Paul Sabatier)

  • M. Casalis

    (Université Paul Sabatier)

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.

Suggested Citation

  • M. Capitaine & M. Casalis, 2007. "Cumulants for Random Matrices as Convolutions on the Symmetric Group, II," Journal of Theoretical Probability, Springer, vol. 20(3), pages 505-533, September.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:3:d:10.1007_s10959-007-0077-y
    DOI: 10.1007/s10959-007-0077-y
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    References listed on IDEAS

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    1. P. Graczyk & G. Letac & H. Massam, 2005. "The Hyperoctahedral Group, Symmetric Group Representations and the Moments of the Real Wishart Distribution," Journal of Theoretical Probability, Springer, vol. 18(1), pages 1-42, January.
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    Cited by:

    1. C. Emily I. Redelmeier, 2011. "Genus Expansion for Real Wishart Matrices," Journal of Theoretical Probability, Springer, vol. 24(4), pages 1044-1062, December.

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