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A central limit theorem on the space of positive definite symmetric matrices. (English) Zbl 0736.60025

A central limit theorem is proved on the space \({\mathcal P}_ n\) of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on \({\mathcal P}_ n\) are defined and investigated. One uses a Taylor expansion of the spherical functions on \({\mathcal P}_ n\).

MSC:

60F05 Central limit and other weak theorems
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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