具有最小调和函数的群，只要你喜欢(附Nicolás Matte Bon的附录)

Pub Date : 2023-11-04 DOI:10.4171/ggd/748

Gideon Amir, Gady Kozma

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引用次数: 3

摘要

对于任意阶的增长$f(n)=o(\log n)$，我们构造了一个有限生成群$G$和一组生成元$S$，使得$G$关于$S$的Cayley图支持一个具有增长$f$的调和函数，但不支持任何增长较慢的调和函数。该构造使用置换环积，其中基群通过其适当选择的Schreier图来定义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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