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VOL. 44 | 2006 Renewal theorems, products of random matrices, and toral endomorphisms
Yves Guivarc'h

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

Abstract

We consider a subsemigroup $T$ of the linear group $G$ of the $d$-dimensional Euclidean space $V$, which is "sufficiently large". We study the orbit closures of $T$ in $V$ and we apply the results to semigroups of endomorphisms of the $d$-dimensional torus. The method uses the knowledge of the potential kernel of the Markov chain on $V$ defined by a probability measure supported on $T$. The condition of being "large" is satisfied for example by a subsemigroup of $SL(V)$, Zariski-dense in $SL(V)$.

Information

Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1119.37008
MathSciNet: MR2277822

Digital Object Identifier: 10.2969/aspm/04410053

Rights: Copyright © 2006 Mathematical Society of Japan

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