  We discuss the $(1+1)$-dimensional wave maps equation with values in a
compact Riemannian manifold $\mathcal{M}$. Motivated by the Gibbs measure
problem, we consider Brownian paths on the manifold $\mathcal{M}$ as initial
data. Our main theorem is the probabilistic local well-posedness of the
associated initial value problem. The analysis in this setting combines
analytic, geometric, and probabilistic methods.
