Abstract: In this talk, I will talk about loop-erased random walk (LERW) in three dimensions. I will

first give an asymptotic estimate on the probability that 3D LERW passes a given point (commonly

referred to as the one-point function). I will then talk about how to apply this estimate to show that 3D

LERW as a curve converges to its scaling limit in natural parametrization. If time permits, I will also talk

about the asymptotics of non-intersection probabilities of 3D LERW with simple random walk. This is a joint work with Daisuke Shiraishi (Kyoto).