A Liouville hyperbolic souvlaki
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Publication:524220
DOI10.1214/17-EJP44zbMATH Open1361.05028arXiv1603.06712MaRDI QIDQ524220
Johannes Carmesin, Bruno Federici, Angelos Georgakopoulos
Publication date: 2 May 2017
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1603.06712
Trees (05C05) Structural characterization of families of graphs (05C75) Relations of low-dimensional topology with graph theory (57M15) Discrete potential theory (31C20) Infinite graphs (05C63) Random walks on graphs (05C81)
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