This article is cited in 4 papers

Short Communications

On Measures with Supports Generated by the Lie Algebra

V. N. Tutubalin

Moscow

Abstract: Consider product $g(n)=g_1\dots g_n$ 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 $G$.

Received: 07.02.1966

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

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