论文标题
随机步行速度是Teichmüller空间的适当功能
Random walk speed is a proper function on Teichmüller space
论文作者
论文摘要
考虑一个具有负欧拉特征的封闭表面$ m $，以及对$ m $的基本组的可接受概率措施，并具有有限的第一刻。与$ M $的Teichmüller空间中的每个点相对应，双曲机平面上有一个相关的随机步行。我们表明，随机步行的速度是$ m $的Teichmüller空间上的适当功能，我们将速度的增长与Teichmüller距离的增长与底线相关联。一个关键的论点是将Gouëzel的旋转技术适应，以对固定组的一系列双曲度度空间的作用。
Consider a closed surface $M$ with negative Euler characteristic, and an admissible probability measure on the fundamental group of $M$ with finite first moment. Corresponding to each point in the Teichmüller space of $M$, there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of $M$, and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel's pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces.
