论文标题
与整数组建造规定的定量轨道等价
Building prescribed quantitative orbit equivalence with the group of integers
论文作者
论文摘要
如果两个组都在共享相同轨道的相同概率空间上采取行动，则它们是轨道的。尤其是Ornstein-Weiss定理意味着所有无限的amenable群体均等同于整数。为了完善无限的amenable群体之间的概念，Delabie，Koivisto，LeMaître和Tessera引入了轨道等效的定量版本。他们进一步获得了使用等值的障碍物对这种等效性的存在。在本文中，我们提出了使用Delabie等人引入的SO所谓的FølnerTigingShifts的整数组，以解决与规定的量化的轨道相等的逆问题。为此，我们使用Brieussel和Zheng定义的对角线产品，并提供具有规定的等法轮廓的组。
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.
