Geodesic
Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon)
Gideon Amir1 orcid ; Gady Kozma2 orcid
1Bar-Ilan University, Ramat Gan, Israel
2Weizmann Institute, Rehovot, Israel
Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 1-24

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DOI

For any order of growth f(n)=o(logn), 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.
DOI : 10.4171/ggd/748
Classification : 20-XX, 60-XX
Mots-clés : groups, Harmonic functions, random walks, wreath products,Schreier graphs

Gideon Amir  1   ; Gady Kozma  2

1 Bar-Ilan University, Ramat Gan, Israel
2 Weizmann Institute, Rehovot, Israel 
Gideon Amir; Gady Kozma. Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon). Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 1-24. doi: 10.4171/ggd/748
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