Measure-theoretic unfriendly colorings
Measure-theoretic unfriendly colorings
复制标题
测量理论不友好的着色
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Clinton T. Conley
中科院分区：
文献类型：
--
作者：
Clinton T. Conley
本文研究了在标准概率空间上求局部有限Borel图的顶点集的可测非友好划分问题。隔离后，这样的分区的存在的充分条件，我们展示了它如何解决动态模拟的问题（弱等价）的图形引起的自由，measurepreserving行动的团体指定有限生成集。作为推论，我们得到了非线性生成群的Cayley图的非线性不变随机不友好染色的存在性。
We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measurepreserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings of Cayley graphs of finitely generated groups.