Central limit theorem on noncompact Riemannian symmetric spaces of rank one
type: Item
instance of: scholarly article
title: Central limit theorem on noncompact Riemannian symmetric spaces of rank one
zbMATH Open document ID: 0891.60024
DOI: 10.1007/BF02882750
published in: Chinese Science Bulletin
publication date: 1998-07-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1091384
zbMATH Keywords: central limit theorem
zbMATH Keywords: symmetric space
zbMATH Keywords: higher rank symmetric space
Wikidata QID: Q115391312
author: Fuliu Zhu
reviewed by: Audrey A. Terras
MaRDI profile type: Publication
cites work: Noneuclidean harmonic analysis, the central limit theorem, and long transmission lines with random inhomogeneities
cites work: Die Resolvente von Delta auf symmetrischen Räumen vom nichtkompakten Typ
cites work: A new proof of a Paley-Wiener type theorem for the Jacobi transform
cites work: Some Transplantation Theorems for the Generalized Mehler Transform and Related Asymptotic Expansions
cites work: Expansions for spherical functions on noncompact symmetric spaces
full work available at URL: https://doi.org/10.1007/bf02882750
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description: scientific article; zbMATH DE number 1091384