A Liouville hyperbolic souvlaki
Combinatorics
2016-03-28 v1 Probability
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.
Cite
@article{arxiv.1603.06712,
title = {A Liouville hyperbolic souvlaki},
author = {Johannes Carmesin and Bruno Federici and Agelos Georgakopoulos},
journal= {arXiv preprint arXiv:1603.06712},
year = {2016}
}