Loop-erased random walk and Poisson kernel on planar graphs (Q717878)

The authors focus on the scalling limit of the loop-erased random walk on graphs embedded into \(\mathbb C\). They show that, if the scalling limit of the random walk is a planar Brownian motion, then the scalling limit of its loop-erasure is a one-parameter family of random continuous curves, known as Schramm-Loewner evolution or SLE\(_2\). The authors main contribution is to show that, for such a graph, the discrete Poisson kernel can be approximated by the continuous one.