Invariant spanning double rays in amenable groups

Agelos Georgakopoulos; Florian Lehner

doi:10.1016/j.disc.2020.112207

Invariant spanning double rays in amenable groups

Agelos Georgakopoulos, Florian Lehner

Institute of Discrete Mathematics (5050)

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

Abstract

A well-known result of Benjamini, Lyons, Peres, and Schramm states that if G is a finitely generated Cayley graph of a group Γ, then Γ is amenable if and only if G admits a Γ-invariant random spanning tree with at most two ends. We show that this is equivalent to the existence of a Γ-invariant random spanning double ray in a power of G.

Original language	English
Article number	112207
Journal	Discrete Mathematics
Volume	344
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2020.112207
Publication status	Published - Feb 2021

Keywords

Cayley graph
invariant random subgraph
spanning double ray
spanning tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2020.112207

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AB - A well-known result of Benjamini, Lyons, Peres, and Schramm states that if G is a finitely generated Cayley graph of a group Γ, then Γ is amenable if and only if G admits a Γ-invariant random spanning tree with at most two ends. We show that this is equivalent to the existence of a Γ-invariant random spanning double ray in a power of G.

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KW - invariant random subgraph

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KW - spanning tree

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Invariant spanning double rays in amenable groups

Abstract

Keywords

ASJC Scopus subject areas

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