Stationary measures and invariant subsets of homogeneous spaces (II)

Benoist, Yves ¹   ; Quint, Jean-François ²

¹ CNRS, Université Paris-Sud Bat.425, 91405 Orsay, France
² CNRS – Université Paris-Nord, LAGA, 93430 Villetaneuse, France

Journal of the American Mathematical Society, Tome 26 (2013) no. 3, pp. 659-734

Résumé

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 $\textrm {Ad }(\Gamma )$ 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.

Détail

DOI : 10.1090/S0894-0347-2013-00760-2

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