论文标题
多端准PMP图的无均可亚福特
Nonamenable subforests of multi-ended quasi-pmp graphs
论文作者
论文摘要
我们证明了A.E.局部有限的准PMP鲍尔图的不违法性，其每个组件至少在基础ra-nikodym Cocycle中至少允许三个不变结束。我们通过构建每个组件至少三个不变末端的Borel亚物物，然后应用Tserunyan和Tserunyan和Tucker-Drob最近对无环准PMP borel图的不舒服性来构建它们的非违法性。我们的主要技术是一种加权循环切割算法，它产生了重量最大的跨越森林。我们还介绍了这个森林的随机版本，该版本概括了自由的最小跨越森林，以捕获渗透理论背景下的非样区。
We prove the a.e. nonamenability of locally finite quasi-pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon--Nikodym cocycle. We witness their nonamenability by constructing Borel subforests with at least three nonvanishing ends per component, and then applying Tserunyan and Tucker-Drob's recent characterization of amenability for acyclic quasi-pmp Borel graphs. Our main technique is a weighted cycle-cutting algorithm, which yields a weight-maximal spanning forest. We also introduce a random version of this forest, which generalizes the Free Minimal Spanning Forest, to capture nonunimodularity in the context of percolation theory.
