Martin boundary covers Floyd boundary

Ilya Gekhtman; Victor Gerasimov; Leonid Potyagailo; Wenyuan Yang

doi:10.1007/s00222-020-01015-z

Martin boundary covers Floyd boundary

Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo, Wenyuan Yang

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	759-809
Number of pages	51
Journal	Inventiones Mathematicae
Volume	223
Issue number	2
DOIs	https://doi.org/10.1007/s00222-020-01015-z
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-020-01015-z

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title = "Martin boundary covers Floyd boundary",

abstract = "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.",

author = "Ilya Gekhtman and Victor Gerasimov and Leonid Potyagailo and Wenyuan Yang",

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doi = "10.1007/s00222-020-01015-z",

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AU - Gekhtman, Ilya

AU - Gerasimov, Victor

AU - Potyagailo, Leonid

AU - Yang, Wenyuan

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Y1 - 2021/2

N2 - 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.

AB - 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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U2 - 10.1007/s00222-020-01015-z

DO - 10.1007/s00222-020-01015-z

M3 - مقالة

SN - 0020-9910

VL - 223

SP - 759

EP - 809

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -

Martin boundary covers Floyd boundary

Abstract

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