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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
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 | ||||||
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| 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: |
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| 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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