论文标题
凯斯滕定理的旋转轨道和拓扑版本的小组动作
Group actions on orbits of an amenable equivalence relation and topological versions of Kesten's theorem
论文作者
论文摘要
我们建立了将统一的liouville属性与可数鲍尔等效关系类别的统一属性结合在一起的结果，并与这种等价关系的合理性联系在一起。我们还将Kesten定理扩展到某些类别的拓扑组，并证明了该定理的适合罪恶群体的定理。此外，我们讨论了Kesten定理的概括与抗浓度的不平等之间的关系，即在可依式等价关系的类别上随机行走的倒轨道。这使我们能够构建一个不满足Kesten定理组合扩展中极限条件的正式波兰群体。
We establish results connecting the uniform Liouville property of group actions on the classes of a countable Borel equivalence relation with amenability of this equivalence relation. We also study extensions of Kesten's theorem to certain classes of topological groups and prove a version of this theorem for amenable SIN groups. Furthermore, we discuss relationship between generalizations of Kesten's theorem and anticoncentration inequalities for the inverted orbits of random walks on the classes of an amenable equivalence relation. This allows us to construct an amenable Polish group that does not satisfy the limit conditions in combinatorial extensions of Kesten's theorem.
