Nonamenable Liouville Graphs
Itai Benjamini, Gady Kozma

TL;DR
This paper constructs a class of non-amenable graphs with Liouville property by adding edges to binary trees, showing they admit no non-constant bounded harmonic functions.
Contribution
It introduces a novel method of augmenting binary trees to produce non-amenable Liouville graphs with specific harmonic function properties.
Findings
Constructed non-amenable Liouville graphs from binary trees
Proved these graphs admit no non-constant bounded harmonic functions
Demonstrated the use of uniform expanders in graph augmentation
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications
