Poisson boundary of GL_d(\Q)

2009/06/30 by Sara Brofferio, Bruno Schapira, Brofferio, Sara +1
Mathematics · #22D40 #28D05 #28D20 #43A05 #60B15 #60J50 #Algebra over a field #Boundary (topology) #Computer science #Construct (python library) #Ergodic theory #FOS: Mathematics #Flag (linear algebra) #Geometry #Mathematical analysis #Mathematics #Multiplicative function #Poisson distribution #Probability (math.PR) #Product (mathematics) #Pure mathematics #Random walk #Statistics #advanced mathematical theories #math.PR #msc:22D40 #msc:28D05 #msc:28D20 #msc:43A05 #msc:60B15 #msc:60J50

paper · pdf · doi:10.48550/arxiv.0906.5548

minor corrections, more details in the introduction

openalex publication_date 2009/06/30 · arxiv created 2009/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product of flag manifolds over the p-adic fields. To this purpose, we prove a law of large numbers using the Oseledets' multiplicative ergodic theorem.

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