  We construct a renewal structure for random walks on surface groups. The
renewal times are defined as times when the random walks enters a particular
type of a cone and never leaves it again. As a consequence, the trajectory of
the random walk can be expressed as an "aligned union" of i.i.d. trajectories
between the renewal times. Once having established this renewal structure, we
prove a central limit theorem for the distance to the origin under exponential
moment conditions. Analyticity of the speed and of the asymptotic variance are
natural consequences of our approach. Furthermore, our method applies to groups
with infinitely many ends and therefore generalizes classic results on central
limit theorems on free groups.
