Poisson boundary for finitely generated groups of rational affinities

2004/03/11 by Sara Brofferio, Brofferio, Sara
Engineering · Mathematics · #22E35 #43A05 #60B99 #60J50 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Probability (math.PR) #math.PR #msc:22E35 #msc:43A05 #msc:60B99 #msc:60J50

paper · pdf · doi:10.48550/arxiv.math/0403197

12 pages, 3 figures

arxiv created 2004/03/11 · openalex publication_date 2004/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The group of affine transformations with rational coefficients, aff(Q), acts naturally on the real line, but also on the p-adic fields. The aim of this note is to show that all these actions are necessary and sufficient to represent bounded μ-harmonic functions for a probability measure μ on aff(Q) that is supported by a finitely generated sub-group, that is to describe the Poisson boundary.

Related

• The Poisson boundary of random rational affinities
• A construction of the measurable Poisson boundary: from discrete to continuous groups
• Non-Realizability of the Poisson Boundary
• Peripheral Poisson boundaries and jointly bi-harmonic functions
• The Poisson boundary of triangular matrices in a number field