Title :

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

Author(s) :

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

Journal title :

L'Enseignement Mathématique

Pages :

341-382

Publisher :

Zürich International Mathematical Society Publishing House

Publication date :

2021-05-05

ISSN :

0013-8584

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL