Groups with minimal harmonic functions as small as you like

Gideon Amir; Gady Kozma; Nicolás Matte Bon

doi:10.4171/GGD/748

Groups with minimal harmonic functions as small as you like

Gideon Amir, Gady Kozma, Nicolás Matte Bon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.4171/GGD/748
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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10.4171/GGD/748

Cite this

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Groups with minimal harmonic functions as small as you like

Abstract

Bibliographical note

Funding

Keywords

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