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arXiv · 2404.18140

The Unique stationary boundary property

Eli Glasner
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Abstract

Let $G$ be a locally compact group and $\mu$ an admissible probability measure on $G$. Let $(B,\nu)$ be the universal topological Poisson $\mu$-boundary of $(G,\mu)$ and $\Pi_s(G)$ the universal minimal strongly proximal $G$-flow. This note is inspired by a recent result of Hartman and Kalantar. We show that for a locally compact second countable group $G$ the following conditions are equivalent: (i) the measure $\nu$ is the unique $\mu$-stationary measure on $B$, (ii) $(B,G) \cong (\Pi_s(G),G)$.

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Eli Glasner. 2024-04-28. The Unique stationary boundary property. https://arxiv.org/abs/2404.18140

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