Lamplighter graphs do not admit harmonic functions of finite energy
Group Theory
2009-07-17 v2 Combinatorics
Abstract
We prove that a lamplighter graph of a locally finite graph over a finite graph does not admit a non-constant harmonic function of finite Dirichlet energy.
Cite
@article{arxiv.0907.1398,
title = {Lamplighter graphs do not admit harmonic functions of finite energy},
author = {Agelos Georgakopoulos},
journal= {arXiv preprint arXiv:0907.1398},
year = {2009}
}