Convergence of loop-erased random walk in the natural parameterization (Q821481)

The main contribution of this paper is that planar loop-erased random walks parameterized by renormalized length converge in the scaling limit to SLE\(_2\) (Schramm-Loewner evolution) parametrized by \(5/4\)-dimensional Minkowski content. In the process of proving this, the authors provide a method for proving similar convergence results for other models converging to SLE and other results of independent interest like two-point estimates, estimates on maximal content, and a separation lemma for two-sided loop-erased random walks.