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

  • Matthieu Dussaule

    Université de Nantes, France
  • Ilya Gekhtman

    Technion - Israeli Institute of Technology, Haifa, Israel
  • Victor Gerasimov

    Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
  • Leonid Potyagailo

    Université Lille, France
The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups cover

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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 , we show that the Martin boundary coincides with the boundary of the truncated space.

Cite this article

Matthieu Dussaule, Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo, The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups. Enseign. Math. 66 (2020), no. 3/4, pp. 341–382

DOI 10.4171/LEM/66-3/4-3