| |
|
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, and Ariel Yadin
Minimal growth harmonic functions on lamplighter groups view print
|
|
| Published: |
July 16, 2017 |
| Keywords: |
Harmonic functions, random walk, lamplighter, wreath product, entropy, Kaimanovich-Vershik |
| Subject: |
60J45, 30F15, 05C63 |
|
|
Abstract
We study the minimal possible growth of harmonic functions on
lamplighters. We find that (Z/2)≀ Z has no sublinear harmonic
functions, (Z/2)≀ Z2 has no sublogarithmic harmonic functions,
and neither has the repeated wreath product
(...b(Z/2≀Z2)≀Z2)≀...b≀Z2. These results have
implications on attempts to quantify the Derriennic-Kaimanovich-Vershik
theorem
|
|
| Acknowledgements
HDC was funded by the IDEX chair of Paris-Saclay as well as the Swiss NSF and the NCCR SwissMap. GK is partially supported by the Israel Science Foundation (grant no. 1369/15) and by the Jesselson Foundation. AY is partially supported by the Israel Science Foundation (grant no. 1346/15).
|
|
| Author information
Itai Benjamini:
The Weizmann Institute of Science, Rehovot, Israel
itai.benjamini@weizmann.ac.il
Hugo Duminil-Copin:
Institut des Hautes Études Scientifiques, Bures-Sur-Yvette, France and Université de Genève, Genève, Switzerland
duminil@ihes.fr
Gady Kozma:
The Weizmann Institute of Science, Rehovot, Israel
gady.kozma@weizmann.ac.il
Ariel Yadin:
Ben-Gurion University of the Negev, Beer Sheva, Israel
yadina@bgu.ac.il
|
|
