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  Martin boundary covers Floyd boundary

Gekhtman, M., Gerasimov, V., Potyagailo, L., & Yang, W. (2021). Martin boundary covers Floyd boundary. Inventiones mathematicae, 223(2), 759-809. doi:10.1007/s00222-020-01015-z.

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 Creators:
Gekhtman, Michael1, Author              
Gerasimov, Victor1, Author              
Potyagailo, Leonid1, Author              
Yang, Wenyuan, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Group Theory, Dynamical Systems, Geometric Topology, Probability
 Abstract: For finitely supported random walks on finitely generated groups $G$ we prove 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 yields new results for relatively hyperbolic groups. Our key estimate relates the Green and Floyd metrics, generalizing results of Ancona for random walks on hyperbolic groups and of Karlsson for quasigeodesics. We then apply these techniques to obtain some results concerning the harmonic measure on the limit sets of geometrically finite isometry groups of Gromov hyperbolic spaces. .

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Language(s): eng - English
 Dates: 2021
 Publication Status: Published in print
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 Rev. Type: Peer
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Title: Inventiones mathematicae
  Abbreviation : Invent. math.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 223 (2) Sequence Number: - Start / End Page: 759 - 809 Identifier: -