论文标题
双曲线组的泊松边界没有瞬间条件
The Poisson boundary of hyperbolic groups without moment conditions
论文作者
论文摘要
我们证明，可以用其双曲线边界识别出有限熵的随机行走的泊松边界，而无需假设量度上的任何力矩条件。我们还将我们的方法扩展到在包含WPD元素的双曲线度量空间上采用异构体作用的组；这适用于大型的非纤维基团，例如相对双曲线组，映射类组和作用于CAT（0）空间的组。
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any moment condition on the measure. We also extend our method to groups with an action by isometries on a hyperbolic metric space containing a WPD element; this applies to a large class of non-hyperbolic groups such as relatively hyperbolic groups, mapping class groups, and groups acting on CAT(0) spaces.
