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Media type:
E-Article
Title:
Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon)
Contributor:
Amir, Gideon;
Kozma, Gady
Published:
European Mathematical Society - EMS - Publishing House GmbH, 2024
Published in:
Groups, Geometry, and Dynamics, 18 (2024) 1, Seite 1-24
Language:
Without Specification
DOI:
10.4171/ggd/748
ISSN:
1661-7207;
1661-7215
Origination:
Footnote:
Description:
For any order of growth f(n)=o(\log n) , weconstruct 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 \mathbb{Z}/2\wr_{X}\Gamma in which the base group \Gamma is defined via its properly chosen action on X .