Minimal growth harmonic functions on lamplighter groups
Probability
2016-07-05 v1 Group Theory
Abstract
We study the minimal possible growth of harmonic functions on lamplighters. We find that has no sublinear harmonic functions, has no sublogarithmic harmonic functions, and neither has the repeated wreath product . These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.
Cite
@article{arxiv.1607.00753,
title = {Minimal growth harmonic functions on lamplighter groups},
author = {Itai Benjamini and Hugo Duminil-Copin and Gady Kozma and Ariel Yadin},
journal= {arXiv preprint arXiv:1607.00753},
year = {2016}
}