ABSTRACT
Loop-erased walk is the self-avoiding random walk derived by erasing loops from simple random walk. In four dimensions, it has been shown that the mean-squared distance of loop-erased walk grows at a rate between n (ln n)1/3 and n (ln n)1/2. In this paper it is proved that the rate is in fact n(ln n)1/3, verifying a conjecture of the author. The technique used to prove this result is the idea of slowly recurrent sets for simple random walk.
