We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on the universal cover of Riemannian manifolds of finite volume with pinched negative curvature. We further provide some ergodic properties of Brownian motions and an application of the central limit theorem to the dynamics of geodesic flows in pinched negative curvature.

中文翻译：

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收缩负曲率中布朗运动的中心极限定理

我们在具有收缩负曲率的有限体积黎曼流形的普遍覆盖上证明了由布朗路径和格林函数的距离引起的随机变量的中心极限定理。我们进一步提供了布朗运动的一些遍历特性，并将中心极限定理应用于收缩负曲率的测地线流动动力学。