Minimal growth harmonic functions on lamplighter groups
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/22)2)…b2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.