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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 1, Pages 154–160 (Mi tvp696)

Short Communications

On Measures with Supports Generated by the Lie Algebra

V. N. Tutubalin

Moscow

Abstract: Consider product $g(n)=g_1…g_n$ of $n$ independent random unimodular matrices with distribution $\mu$ (which is supposed to be absolutely continuous with respect to the Haar measure on corresponding group $G$). If these matrices are real it is possible that the distributions of $g(n)$ and $g(n+1)$ be quite different even for large $n$. This fact depends on the existence of periodicity in a Markov chain. In this paper it is proved that the periodicity cannot exist if $\mu(\exp L)>0$ where $L$ is the Lie algebra of $G$.

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English version:
Theory of Probability and its Applications, 1967, 12:1, 134–138

Bibliographic databases:

Citation: V. N. Tutubalin, “On Measures with Supports Generated by the Lie Algebra”, Teor. Veroyatnost. i Primenen., 12:1 (1967), 154–160; Theory Probab. Appl., 12:1 (1967), 134–138

Citation in format AMSBIB
\Bibitem{Tut67} \by V.~N.~Tutubalin \paper On Measures with Supports Generated by the Lie Algebra \jour Teor. Veroyatnost. i Primenen. \yr 1967 \vol 12 \issue 1 \pages 154--160 \mathnet{http://mi.mathnet.ru/tvp696} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=219102} \zmath{https://zbmath.org/?q=an:0183.19304|0158.16804} \transl \jour Theory Probab. Appl. \yr 1967 \vol 12 \issue 1 \pages 134--138 \crossref{https://doi.org/10.1137/1112017}