Infinite stationary measures of co-compact group actions

2024/10/31 by Alhalimi, Mohammedsaid, Hutchcroft, Tom, Pan, Minghao +2 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.23600

Abstract

Let Γ be a finitely generated group, and let μ be a nondegenerate, finitely supported probability measure on Γ. We show that every co-compact Γ action on a locally compact Hausdorff space admits a nonzero μ-stationary Radon measure. The main ingredient of the proof is a stationary analogue of Tarski's theorem: we show that for every nonempty subset A ⊆ Γ there is a μ-stationary, finitely additive measure on Γ that assigns unit mass to A.

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