Abstract
For any order of growth f (n) = o(log n), we construct a finitely-generated group G and a set of generators S such that the Cayley graph of G with respect to S supports a harmonic function with growth f but does not support any harmonic function with slower growth. The construction uses permutational wreath products Z/2 ≀X Γ in which the base group Γ is defined via its properly chosen action on X .
| Original language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Groups, Geometry, and Dynamics |
| Volume | 18 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2023 European Mathematical Society.
Funding
Funding. While performing this research, Gideon Amir was supported by the Israel Science Foundation grant #1471/11. Gady Kozma was supported by the Israel Science Foundation grant #1369/15 and by the Jesselson Foundation.
| Funders | Funder number |
|---|---|
| Jesselson Foundation | |
| Israel Science Foundation | 1369/15, 1471/11 |
Keywords
- Harmonic functions
- Schreier graphs
- group actions
- random walks
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