| dc.creator | Carmesin, Johannes | |
| dc.creator | Federici, B | |
| dc.creator | Georgakopoulos, A | |
| dc.date.accessioned | 2017-03-05 | |
| dc.date.accessioned | 2018-11-24T23:27:19Z | |
| dc.date.available | 2017-06-01T12:36:54Z | |
| dc.date.available | 2018-11-24T23:27:19Z | |
| dc.date.issued | 2017-04-25 | |
| dc.identifier | https://www.repository.cam.ac.uk/handle/1810/264570 | |
| dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3961 | |
| dc.description.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 Gábor Pete and Gourab Ray, our construction is extended to yield a unimodular graph with the above properties. | |
| dc.language | en | |
| dc.publisher | Institute of Mathematical Statistics | |
| dc.publisher | Electronic Journal of Probability | |
| dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
| dc.rights | http://creativecommons.org/licenses/by/4.0/ | |
| dc.rights | Attribution 4.0 International | |
| dc.rights | Attribution 4.0 International | |
| dc.subject | Liouville property | |
| dc.subject | hyperbolic graph | |
| dc.subject | infinite graph | |
| dc.subject | amenability | |
| dc.subject | transience | |
| dc.subject | flow | |
| dc.subject | harmonic function | |
| dc.title | A Liouville hyperbolic souvlaki | |
| dc.type | Article | |
