Abstract
We study the minimal possible growth of harmonic functions on lamplighters. We find that (Z/2) (Formula presented.) Z2 has no sublinear harmonic functions, (Z/2) (Formula presented.) Z2 has no sublogarithmic harmonic functions, and neither has the repeated wreath product (… (Z/2 (Formula presented.) Z2) (Formula presented.) Z2) (Formula presented.) … (Symbol found) Z2. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem.
Original language | English |
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Pages (from-to) | 833-858 |
Number of pages | 26 |
Journal | New York Journal of Mathematics |
Volume | 23 |
State | Published - 16 Jul 2017 |
Keywords
- Entropy
- Harmonic functions
- Kaimanovich-Vershik
- Lamplighter
- Random walk
- Wreath product
ASJC Scopus subject areas
- General Mathematics