Probability laws for the distribution of geometric lengths when sampling by a random walk in a Fuchsian fundamental group

Peter S. Park

Let $S=\Gamma \backslash \mathbb{H}$ be a hyperbolic surface of finite topological type, such that the Fuchsian group $\Gamma \le {\mathrm{PSL}}_2(\mathbb{R})$ is non-elementary, and consi…