Titre :

The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups

Auteur(s) :

Dussaule, Matthieu [Auteur]
Gekhtman, Ilya [Auteur]
Gerasimov, Victor [Auteur]
Potyagailo, Leonid [Auteur]
Département de mathématiques [Lille]

Titre de la revue :

L'Enseignement Mathématique

Pagination :

341-382

Éditeur :

Zürich International Mathematical Society Publishing House

Date de publication :

2021-05-05

ISSN :

0013-8584

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Given a probability measure on a finitely generated group, its Martinboundary is a way to compactify the group using the Green's functionof the corresponding random walk.We give a complete topological characterization ...
Lire la suite >Given a probability measure on a finitely generated group, its Martinboundary is a way to compactify the group using the Green's functionof the corresponding random walk.We give a complete topological characterization of the Martin boundary of finitely supported random walks on relatively hyperbolic groups with virtually abelian parabolic subgroups. In particular, in the case of nonuniform lattices in the real hyperbolic space $\mathbb{H}^{n}$, we show that the Martin boundary coincides with the $CAT(0)$ boundary of the truncated space.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL