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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Stationary measures and invariant subsets of homogeneous spaces (II)


Authors: Yves Benoist and Jean-François Quint
Journal: J. Amer. Math. Soc. 26 (2013), 659-734
MSC (2010): Primary 22E40, 37C40, 37C85
Published electronically: January 11, 2013
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Abstract: Let $ G$ be a real Lie group, $ \Lambda $ a lattice of $ G$, $ \mu $ a compactly supported probability measure on $ G$, and $ \Gamma $ the subgroup generated by the support of $ \mu $. We prove that, when the Zariski closure of the adjoint group $ {\rm Ad }(\Gamma )$ is semisimple with no compact factor, every $ \mu $-ergodic $ \mu $-stationary probability measure on $ G/\Lambda $ is homogeneous. We also prove similar results for $ p$-adic Lie groups.


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Additional Information

Yves Benoist
Affiliation: CNRS, Université Paris-Sud Bat.425, 91405 Orsay, France
Email: yves.benoist@math.u-psud.fr

Jean-François Quint
Affiliation: CNRS – Université Paris-Nord, LAGA, 93430 Villetaneuse, France
Email: quint@math.univ-paris13.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00760-2
PII: S 0894-0347(2013)00760-2
Received by editor(s): July 8, 2011
Received by editor(s) in revised form: October 9, 2012
Published electronically: January 11, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.