dc.contributor.author Dussaule, Matthieu dc.contributor.author Gekhtman, Ilya dc.contributor.author Gerasimov, Victor dc.contributor.author Potyagailo, Leonid dc.date.accessioned 2018-03-19T13:04:47Z dc.date.available 2018-03-19T13:04:47Z dc.date.issued 2018-03-19 dc.identifier.uri http://publications.mfo.de/handle/mfo/1356 dc.description.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 ${\mathcal H}^n$, 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. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,03 dc.title The Martin Boundary of Relatively Hyperbolic Groups with Virtually Abelian Parabolic Subgroups en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-03 local.scientificprogram Research in Pairs 2017 en_US local.series.id OWP-2018-03 en_US dc.identifier.urn urn:nbn:de:101:1-2018032020486 dc.identifier.ppn 1654584630
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