The asymptotics of spherical functions and the central limit theorem on symmetric cones

Zhang, Genkai

Annales de l'Institut Fourier, Tome 45 (1995) no. 2, pp. 565-575.

On démontre un théorème central limite pour certaines variables aléatoires sur le cône symétrique d’une algèbre de Jordan formellement réelle. Le résultat prolonge des résultats de Richards et Terras sur le cône des matrices réelles définies positives $n\times n$.

We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite $n\times n$ matrices.

[A] J. Arazy, Personal communication.

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