3 problems

Let $\Gamma<\mathrm{SL}_N(\mathbb{R})$ be a discrete subgroup, and let the random walk on $\Gamma$ have finite support. Its hitting measure is a measure on the boundary at infinity…

Let $S$ be the surface under consideration, let $p\in S$, and let $\mu$ be an admissible measure on $\pi_1(S,p)$ with finite first moment and finite support. For a metric $\rho$, v…

Let $(X_n)$ be a finite-range admissible random walk generated by a probability measure $\mu$ on a cocompact Fuchsian group $\Gamma$, and let $\nu_\mu$ be its hitting measure on th…