  Loop-erased random walk, abbreviated LERW, is one of the most well-studied
critical lattice models. It is the self-avoiding random walk one gets after
erasing the loops from a simple random walk in order or alternatively by
considering the branches in a uniformly chosen spanning tree. This paper proves
that planar LERW parametrized by renormalized length converges in the lattice
size scaling limit to SLE(2) parametrized by 5/4-dimensional Minkowski content.
In doing this we also provide a method for proving similar convergence results
for other models converging to SLE. Besides the main theorem, several of our
results about LERW are of independent interest: for example, two-point
estimates, estimates on maximal content, and a "separation lemma".
