单模随机双曲流形的拓扑与动力学
Topology and dynamics of unimodular random hyperbolic manifolds
AI总结：
研究单模随机双曲流形端点空间与测地线流动力学关系，证明有两个无限体积端点意味着递归，无限多个则意味着正漂移和熵，还给出适用于确定性双曲流形的暂态准则，方法基于德劳内图和容量概念。
AI中文摘要：
我们研究了单模随机双曲流形的端点空间与其测地线流动力学之间的关系。我们表明，具有两个无限体积的端点意味着递归，而具有无限多个这样的端点意味着正漂移和熵。我们还提供了一个适用于确定性双曲流形的暂态准则。我们的方法依赖于研究点过程上的德劳内图和容量的解析概念。
英文摘要：
We investigate the relationship between the space of ends of a unimodular random hyperbolic manifold and the dynamics of its geodesic flow. We show that having two ends of infinite volume implies recurrence, while having infinitely many such ends implies positive drift and entropy. We also provide a transience criterion which applies to deterministic hyperbolic manifolds. Our method relies on studying Delaunay graphs over point processes and on the analytic notion of capacity.
