Lukas Schoug: Level lines of the GFF and c = 1 degenerate conformal blocks

Abstract: We discuss the link patterns of a class of level lines of the GFF. In particular, we determine the probabilities of the various link patterns arising and relate these to the c = 1 degenerate conformal blocks. Moreover, we prove that said family of level lines satisfies the resampling property. One consequence of our analysis is the existence of multiple SLE(4) where several curves are allowed to start/terminate at the same point. We further prove the uniqueness of multiple SLE(4) with these patterns.

This is based on joint work with Alex Karrila and Eveliina Peltola.