On fluctuations of the drift in hyperbolic groups

Let $Γ$ refer to a convex-cocompact group of isometries of a CAT($-1$) space $X$ and $Y \to X/Γ$ to a Galois cover with a word-hyperbolic group of deck transformations. We show that, for almost every geodesic $ξ$ with respect to the Bowen-Margulis-Sullivan measure on the lift of $X/Γ$, there exist $