Convergence in distribution of the product of random variables from an independent sample on a compact algebraic group

O. G. Styrt

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arXiv · 2211.10071

Convergence in distribution of the product of random variables from an independent sample on a compact algebraic group

O. G. Styrt

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Abstract

An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution exists and is uniform on the support of the parent distribution if a random variable with such a distribution does not belong with the unit probability to any non-trivial coset over an algebraic subgroup that lies in its normalizer; otherwise, it does not exist.

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O. G. Styrt. 2022-11-18. Convergence in distribution of the product of random variables from an independent sample on a compact algebraic group. https://arxiv.org/abs/2211.10071

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