Levi Haunschmid-Sibitz: Near-critical Dimers and Massive SLE

Abstract:

The uniform dimer model is a classical model from statistical mechanics and one of the few models where conformal invariance has been established. We consider an near-critical weighted version of this model and connect it via the Temperley Bijection and Wilson's Algorithm to a loop-erased random walk. The scaling limit of this walk is (a generalization of) massive SLE_2 as constructed by Markarov and Smirnov and might be of independent interest.

In the talk after sketching the connection between the dimer model and the loop-erased random walk, I will focus on this walk and its scaling limit. First I will present some exact Girsanov identities that help connect a random walk with mass with a random walk with drift, and then I will show some of the techniques and difficulties that go into defining the continuum limit.