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arXiv · 1605.07593

Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)

Gideon Amir·Gady Kozma
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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 in which the base group is defined via its properly chosen Schreier graph.

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Gideon Amir, Gady Kozma. 2017-02-05. Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon). https://arxiv.org/abs/1605.07593

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