The Poisson boundary of random rational affinities

2004/03/11 by Sara Brofferio, Brofferio, Sara
Mathematics · #22E35 #43A05 #60B99 #60J50 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories #math.PR #msc:22E35 #msc:43A05 #msc:60B99 #msc:60J50

paper · pdf · doi:10.48550/arxiv.math/0403198

13 pages

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 acts naturally on the real line, but also on the p-adic fields. The aim of this note is to show that, for random walks whose laws have a finite first moment, all these actions are necessary and sufficient to describe the Poisson boundary, which is in fact the product of all the fields that contract in mean.

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