Strong path convergence from Loewner driving function convergence (Q414278)

The Loewner differential equation, provided by Loewner in 1923, relates a planar self-avoiding curve to a real-valued continuous function (the ``Loewner driving function'') via conformal mappings. The authors introduce ``uniform convergence'' as a short-hand for ``convergence in law'' with respect to the uniform metric, when speaking of random curves. The goal of the present article is to provide a more general criterion for deducing uniform convergence, which is less dependent on specific features of the model at hand.