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An application of the method of moments to the central limit theorem on hyperbolic spaces

  • Herbert Heyer
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

On the hyperbolic spaces of the form G/K a fairly complete theory of spherical functions is available in order to study Fourier transforms of K-biinvariant probability measures on G. The differentiability of this Fourier transform enables us to introduce the notion of variance. Moreover, continuous convolution semigroups of probability measures admit a Lévy-Khintchine representation, and so Gaussian semi-groups can be defined via their Fourier transforms. The aim of our discussion is to establish sufficient conditions in terms of variances for a triangular system of K-biinvariant probability measures on G to converge towards a Gaussian measure.

Keywords

Symmetric Space Central Limit Theorem Hyperbolic Space Spherical Function Triangular System 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Herbert Heyer
    • 1
  1. 1.Mathematisches Institut der UniversitätTübingen

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