无矩条件下双曲群的泊松边界
群论
2022-11-30 v2 动力系统
几何拓扑
概率论
摘要
我们证明了非初等双曲群上具有限熵的随机游走的泊松边界可与其双曲边界等同，且不对测度作任何矩条件假设。我们还将方法推广到在含 WPD 元素的双曲度量空间上以等距作用作用的群；这适用于一大类非双曲群，如相对双曲群、映射类群，以及作用在 CAT(0) 空间上的群。
引用
@article{arxiv.2209.02114,
title = {The Poisson boundary of hyperbolic groups without moment conditions},
author = {Kunal Chawla and Behrang Forghani and Joshua Frisch and Giulio Tiozzo},
journal= {arXiv preprint arXiv:2209.02114},
year = {2022}
}
备注
23 pages. Changes in the new version: we included Theorem 1.2, which now applies to all groups with a WPD element, and its applications in Corollary 1.3. The proof is in Section 5. For the sake of exposition, we also added Section 3.1, explaining the concept of pivots for free groups