构建具有整数群的指定定量轨道等价性
Building prescribed quantitative orbit equivalence with the group of integers
AI总结：
本文研究整数群的轨道等价性，利用Følner瓷砖移位和对角积方法，解决给定群的定量轨道等价性问题。
摘要：
两个群轨道等价当它们在同一个概率空间上的作用具有相同轨道。Ornstein-Weiss定理表明所有无限可算群都与整数群轨道等价。Delabie等人引入了轨道等价的定量版本，并利用等周轮廓提出障碍。本文通过Følner瓷砖移位和对角积方法，解决给定群的定量轨道等价性问题。
英文摘要：
Two groups are orbit equivalent if they both admit an action on a same probability space that share the same orbits. In particular the Ornstein-Weiss theorem implies that all infinite amenable groups are orbit equivalent to the group of integers. To refine this notion between infinite amenable groups Delabie, Koivisto, Le Maître and Tessera introduced a quantitative version of orbit equivalence. They furthermore obtained obstructions to the existence of such equivalence using the isoperimetric profile. In this article we offer to answer the inverse problem (find a group being orbit equivalent to a prescribed group with prescribed quantification) in the case of the group of integers using the so called Følner tiling shifts introduced by Delabie et al. To do so we use the diagonal products defined by Brieussel and Zheng giving groups with prescribed isoperimetric profile.
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