Stationary measures and invariant subsets of homogeneous spaces (II)

Benoist, Yves; Quint, Jean-François

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

Stationary measures and invariant subsets of homogeneous spaces (II)
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by Yves Benoist and Jean-François Quint

J. Amer. Math. Soc. 26 (2013), 659-734

DOI: https://doi.org/10.1090/S0894-0347-2013-00760-2

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

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