论文标题
随机步行和排名在CAT（0）空间上的一个等法
Random walks and rank one isometries on CAT(0) spaces
论文作者
论文摘要
令$ g $为离散的组，$ g $ $ g $ $ $ $ $ $ x $ a a a a pure cat（0）空间。我们表明，如果$ g $在$ x $上以排名一个元素非元素作用，那么pushforward $ \ {z_n o \} _ n $ to $μ$生成的随机步行的$ x $几乎可以肯定地肯定地将其排名一点点。我们还表明，在这种情况下，在视觉边界$ \ partial_ \ infty x $的$ x $上有一个独特的固定度量，随机步行的漂移几乎肯定是积极的。
Let $G$ be a discrete group, $μ$ a measure on $G$ and $X$ a proper CAT(0) space. We show that if $G$ acts non-elementarily with a rank one element on $X$, then the pushforward $\{Z_n o \}_n$ to $X$ of the random walk generated by $μ$ converges almost surely to a rank one point of the boundary. We also show that in this context, there is a unique stationary measure on the visual boundary $\partial_\infty X$ of $X$, and that the drift of the random walk is almost surely positive.
