Martin boundary covers Floyd boundary

Ilya Gekhtman Department of Mathematics, Technion-Israeli Institute of Technology, 32000 Haifa, Israel Victor Gerasimov Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Caixa Postal 702, 30161-970 Brasil Leonid Potyagailo UFR de Mathématiques, Université de Lille, 59655 Villeneuve d’Ascq, France Wenyuan Yang Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China

Dynamical Systems Geometric Analysis and Geometric Topology Group Theory and Lie Theory Probability mathscidoc:2203.11005

Inventiones Mathematicae, 223, 759-809, 2021.1
For a random walk on a finitely generated group G we obtain a generalization of a classical inequality of Ancona. We deduce as a corollary that the identity map on G extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This provides new results for Martin compactifications of relatively hyperbolic groups.
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  title={Martin boundary covers Floyd boundary},
  author={Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo, and Wenyuan Yang},
  booktitle={Inventiones Mathematicae},
Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo, and Wenyuan Yang. Martin boundary covers Floyd boundary. 2021. Vol. 223. In Inventiones Mathematicae. pp.759-809.
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