Invariant spanning double rays in amenable groups

Agelos Georgakopoulos, Florian Lehner

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number112207
JournalDiscrete Mathematics
Issue number2
Publication statusPublished - Feb 2021


  • 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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