UVictoria Probability and Dynamics Seminar: Leonie Papon

I will present a coupling between a massive planar Gaussian free field (GFF) and a random curve in which the curve can be interpreted as the level of the field. This coupling is constructed by reweighting the law of the standard GFF-SLE_4 coupling. I will then show that in this coupling, the marginal law of the curve is that of a massive version of SLE_4, called massive SLE_4. This law on curves was orignally introduced by Makarov and Smirnov to describe the scaling limit of a massive version of the harmonic explorer.