Comptes Rendus
Théorie des groupes
Mesures stationnaires et fermés invariants des espaces homogènes
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 9-13.

Soient G un groupe de Lie réel simple, Λ un réseau de G et Γ un sous-groupe Zariski dense de G. On montre que toute orbite de Γ dans le quotient X=G/Λ est finie ou dense. Soit μ une probabilité sur G dont le support est compact et engendre un sous-groupe Zariski dense de G. On montre que toute probabilité μ-stationnaire et μ-ergodique sur X est de support fini ou est G-invariante.

Let G be a real simple Lie group, Λ be a lattice of G and Γ be a Zariski dense subgroup of G. We prove that every Γ-orbit in the quotient X=G/Λ is either finite or dense. Let μ be a probability measure on G whose support is compact and generates a Zariski dense subgroup of G. We prove that every μ-ergodic μ-stationary probability measure on X either has finite support or is G-invariant.

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DOI : 10.1016/j.crma.2008.11.001

Yves Benoist 1 ; Jean-François Quint 2

1 CNRS – Université Paris-Sud, 91405 Orsay cedex, France
2 CNRS – Université Paris-Nord, 93430 Villetaneuse, France
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Yves Benoist; Jean-François Quint. Mesures stationnaires et fermés invariants des espaces homogènes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 9-13. doi : 10.1016/j.crma.2008.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.001/

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