A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when (1) the step distribution has exponential tail and (2) the action on $X$ is acylindrical.

中文翻译：

---

弱双曲群中具有指数衰减的线性进展

当步长分布支持两个独立的氧杂环丁烷时，在可分离的测地双曲度量空间$ X $上的随机游走$ w_n $收敛到边界$ \ partial X $。特别地，随机游走产生线性正进展。当（1）阶跃分布具有指数尾部并且（2）对$ X $的作用为圆柱状时，已知进度是线性的且具有指数衰减。