Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon)
Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon)
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具有最小谐波函数的组，小到你喜欢的大小（附有尼古拉斯·马特·邦（Nicolás Matte Bon）的附录）
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发表时间：
2016
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通讯作者：
G. Kozma
中科院分区：
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作者：
Gideon Amir;G. Kozma
对于任何增长阶$f(n)=o(log n)$，我们构造一个有限生成群$G$和一组生成器$S$，使得$G$相对于$S$的凯莱图支持具有增长$f$的调和函数，但不支持任何增长较慢的调和函数。该结构使用排列花环产品，其中基组通过正确选择的施赖尔图来定义。
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.