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

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics 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。

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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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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.