2000 character limit reached
Minimal growth harmonic functions on lamplighter groups (1607.00753v1)
Published 4 Jul 2016 in math.PR and math.GR
Abstract: We study the minimal possible growth of harmonic functions on lamplighters. We find that $(\mathbb{Z}/2)\wr \mathbb{Z}$ has no sublinear harmonic functions, $(\mathbb{Z}/2)\wr \mathbb{Z}2$ has no sublogarithmic harmonic functions, and neither has the repeated wreath product $(\dotsb(\mathbb{Z}/2\wr\mathbb{Z}2)\wr\mathbb{Z}2)\wr\dotsb\wr\mathbb{Z}2$. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.