Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dussaule, MattieuGekhtman, IlyaGerasimov, VictorPotyagailo, Leonid2024-10-162024-10-162018https://oa.tib.eu/renate/handle/123456789/16883https://doi.org/10.34657/15905Given 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 Hⁿ, 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.eng510Report