Central limit theorem on noncompact Riemannian symmetric spaces of rank one
The author generalizes the central limit theorem for rotation-invariant random variables with values in the Poincaré upper half plane to all noncompact Riemannian symmetric spaces of rank 1. The proof uses an asymptotic formula for spherical functions on the symmetric space and formulas for the heat kernel of \textit{N. Lohoué} and \textit{Th. Rychener} [Comment. Math. Helv. 57, 445-468 (1982; 505.53022)]. More recently the reviewer [J. Multivariate Anal. 23, No. 1, 13-36 (1987; Zbl 0627.43009)] and \textit{D. St. P. Richards} [ibid. 29, No. 2, 326-332 (1989; Zbl 0681.60026)] have generalized the result to the higher rank symmetric space of positive definite \(n\times n\) real matrices.
scientific article; zbMATH DE number 1091384