论文标题
迪里奇的随机步行
The Dirichlet random walk
论文作者
论文摘要
在本文中，我们定义并研究了紧凑型歧管的Galoisian封面的随机过程。该过程的连续位置是通过在上一个dirichlet域中统一选择的点来递归定义的。我们在这样一个过程中证明了凯斯滕定理：随机步行的逃逸率是积极的，并且只有当盖子不可正常时。我们还在详细研究中进行了更多研究，即甲板组是Gromov双曲线，显示了轨迹边界的几乎确定的收敛以及逃逸率的中心限制定理
In this article we define and study a stochastic process on Galoisian covers of compact manifolds. The successive positions of the process are defined recursively by picking a point uniformly in the Dirichlet domain of the previous one. We prove a theorem à la Kesten for such a process: the escape rate of the random walk is positive if and only if the cover is non amenable. We also investigate more in details the case where the deck group is Gromov hyperbolic, showing the almost sure convergence to the boundary of the trajectory as well as a central limit theorem for the escape rate
