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Asymptotics of special functions and the central limit theorem on the space [Weierstrass p]n of positive n - n matrices

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  • Terras, Audrey

Abstract

When n = 3 using methods similar to the author's (1984, J. Multivariate Anal.15, 261-276), an analog of the central limit theorem is obtained for rotation-invariant random variables on the space[Weierstrass p]n of positive n - n real matrices (the symmetric space of the general linear group GL(n,[real]) of n - n nonsingular real matrices). The necessary results from harmonic analysis onPn are sketched.

Suggested Citation

  • Terras, Audrey, 1987. "Asymptotics of special functions and the central limit theorem on the space [Weierstrass p]n of positive n - n matrices," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 13-36, October.
    • Handle: RePEc:eee:jmvana:v:23:y:1987:i:1:p:13-36
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    Cited by:

    1. Michael Voit, 2017. "Dispersion and Limit Theorems for Random Walks Associated with Hypergeometric Functions of Type BC," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1130-1169, September.
    2. Armin Schwartzman, 2016. "Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices," International Statistical Review, International Statistical Institute, vol. 84(3), pages 456-486, December.
    3. P. Sawyer, 2001. "The Central Limit Theorem on SO0(p, q)/SO(p)×SO(q)," Journal of Theoretical Probability, Springer, vol. 14(3), pages 857-866, July.

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