The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups
Group Theory
2018-01-29 v2 Dynamical Systems
Geometric Topology
Probability
Abstract
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of 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 H n , we show that the Martin boundary coincides with the CAT (0) boundary of the truncated space, and thus when n = 3, is homeomorphic to the Sierpinski carpet.
Keywords
Cite
@article{arxiv.1711.11307,
title = {The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups},
author = {Matthieu Dussaule and Ilya Gekhtman and Victor Gerasimov and Leonid Potyagailo},
journal= {arXiv preprint arXiv:1711.11307},
year = {2018}
}