A Liouville hyperbolic souvlaki

Johannes Carmesin, Bruno Federici, Agelos Georgakopoulos

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We construct a transient bounded-degree graph no transient subgraph of which embeds in any surface of finite genus. Moreover, we construct a transient, Liouville, bounded-degree, Gromov--hyperbolic graph with trivial hyperbolic boundary that has no transient subtree. This answers a question of Benjamini. This graph also yields a (further) counterexample to a conjecture of Benjamini and Schramm.
Original languageEnglish
Pages (from-to)1-19
JournalElectronic Journal of Probability
Issue number36
Publication statusPublished - 2017


  • math.CO
  • math.PR
  • 57M15, 05C63, 05C81, 31C20


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