Fredrik Viklund: Scaling limit of the probability that a loop-erased random walk uses a given edge

Abstract.  Loop-erased random walk (LERW) is a random self-avoiding walk obtained by erasing the loops of a simple random walk. In the talk I will discuss a proof of the following result: The renormalized probability that a LERW in (a lattice approximation of) a simply connected domain uses a given interior edge, converges in the scaling limit to an explicit conformally covariant quantity: the so-called SLE_2 Green's function. This is based on joint work with Christian Benes (CUNY) and Greg Lawler (Chicago).