论文标题
可数等效关系的共谱半径
Co-spectral radius for countable equivalence relations
论文作者
论文摘要
我们定义包含物的共谱半径$ \ MATHCAL {S} \ LEQ \ MATHCAL {R} $的离散，概率测量值的等价关系，是在环境关系上生成随机行走的采样指数。共同光谱半径类似于$ g/h $的随机步行频谱半径，用于包含$ h \ h \ leq g $ of组。为了证明，我们开发了一种更通用的2-3方法，我们在另一项关于单模型随机生根树生长的工作中使用。我们使用这种方法来表明，对于任意的单型界面的界面图，存在步行生长。我们还研究了共光谱半径如何用于高铁关系，并讨论可以使用共谱半径来定义的新的关键指数。
We define the co-spectral radius of inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a generating random walk on the ambient relation. The co-spectral radius is analogous to the spectral radius for random walks on $G/H$ for inclusion $H\leq G$ of groups. For the proof, we develop a more general version of the 2-3 method we used in another work on the growth of unimodular random rooted trees. We use this method to show that the walk growth exists for an arbitrary unimodular random rooted graph of bounded degree. We also investigate how the co-spectral radius behaves for hyperfinite relations, and discuss new critical exponents for percolation that can be defined using the co-spectral radius.
