English

Nonamenable Liouville Graphs

Metric Geometry 2010-10-19 v1 Probability

Abstract

Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.

Keywords

Cite

@article{arxiv.1010.3365,
  title  = {Nonamenable Liouville Graphs},
  author = {Itai Benjamini and Gady Kozma},
  journal= {arXiv preprint arXiv:1010.3365},
  year   = {2010}
}

Comments

5 pages, 4 conjectures

R2 v1 2026-06-21T16:29:30.644Z