A construction of the measurable Poisson boundary: from discrete to continuous groups. - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2017

A construction of the measurable Poisson boundary: from discrete to continuous groups.

Résumé

Let Γ be a dense countable subgroup of a locally compact continuous group G, and μ a probability measure on Γ. Two spaces of harmonic functions are naturally associated with μ: the space of μ-harmonic functions on the countable group Γ and the space of μ-harmonic functions seen as functions on G defined a.s. with respect to its Haar measure λ. Correspondingly we have two natural Poisson boundaries: the Γ-Poisson boundary and the G-Poisson bounary. Since boundaries on the countable group are quite well understood, a natural question is to ask how G-boundary is related to the Γ-boundary. ``In this chapter we introduce a general technique that allows us to build the G-Poisson boundary from the Γ-boundary. As an application, we determine the Poisson boundary of the closure of the Baumslag-Solitar group in the group of real matrices. In particular we show that, under suitable moment conditions and assuming that the action on R is not contracting, this boundary is the p-solenoid
Fichier non déposé

Dates et versions

hal-04214921 , version 1 (22-09-2023)

Identifiants

  • HAL Id : hal-04214921 , version 1

Citer

Sara Brofferio. A construction of the measurable Poisson boundary: from discrete to continuous groups.. Groups, graphs and random walks, 2017, 978-1-316-60440-3. ⟨hal-04214921⟩
15 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More