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A Liouville hyperbolic souvlaki

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Carmesin, J., Federici, Bruno and Georgakopoulos, Agelos (2017) A Liouville hyperbolic souvlaki. Electronic Journal of Probability, 22 . 23. doi:10.1214/17-EJP44

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Official URL: http://doi.org/10.1214/17-EJP44

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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. In an appendix by G´abor Pete and Gourab Ray, our construction is extended to yield a unimodular graph with the above properties.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Sturm-Liouville equation, Hyperbolic groups, Infinite groups
Journal or Publication Title: Electronic Journal of Probability
Publisher: University of Washington. Dept. of Mathematics
ISSN: 1083-6489
Official Date: 25 May 2017
Dates:
DateEvent
25 May 2017Available
5 March 2017Accepted
Volume: 22
Number of Pages: 19
Article Number: 23
DOI: 10.1214/17-EJP44
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: Engineering and Physical Sciences Research Council (EPSRC), Horizon 2020 (European Commission) (H2020), European Research Council (ERC)
Grant number: EP/L505110/1 (EPSRC), 639046 (ERC)
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