A Liouville hyperbolic souvlaki

Johannes Carmesin; Bruno Federici; Agelos Georgakopoulos

doi:10.1214/17-EJP44

A Liouville hyperbolic souvlaki

Johannes Carmesin, Bruno Federici, Agelos Georgakopoulos

Mathematics

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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.

Original language	English
Pages (from-to)	1-19
Journal	Electronic Journal of Probability
Volume	22
Issue number	36
DOIs	https://doi.org/10.1214/17-EJP44
Publication status	Published - 2017

Keywords

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

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10.1214/17-EJP44Licence: Creative Commons: Attribution (CC BY)

1603.06712v1
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Carmesin_et_al_Lioville_hyperbolic_souvlaki_EJPFinal published version, 537 KBLicence: Creative Commons: Attribution (CC BY)

https://arxiv.org/abs/1603.06712

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AB - 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.

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JO - Electronic Journal of Probability

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A Liouville hyperbolic souvlaki

Abstract

Keywords

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