The Unique stationary boundary property

2024/04/28 by Eli Glasner, Glasner, Eli
Computer Science · Engineering · #22D40 #37A50 #37B05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2404.18140

openalex publication_date 2024/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a locally compact group and μ an admissible probability measure on G. Let (B,ν) be the universal topological Poisson μ-boundary of (G,μ) and Π_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 ν is the unique μ-stationary measure on B, (ii) (B,G) ≅ (Π_s(G),G).

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