The uniform distribution on dimer configurations is one of the most classical two-dimensional lattice models in statistical physics. In the past decades there has been a lot of progress in the study of this model, in particular the existance of a limit shape and the conformal invariance of fluctations are important results in probability.
In this talk I will talk about an off-critical version of this model, in which weights attached to edges converge to the critical value as a scaling parameter goes to zero. A version of this model was first introduced in 2012 by Chhita, where its fluctuations were shown to be non-Gaussian. We study this and a related model in finite volume and Temperleyan boundary conditions. Through the Temperley bijection we find a connection to massive Schramm Loewner evolution, as first described by Markarov and Smirnov in 2010 and recently revisited by Chelkak and Wan in 2019. Along the way we also prove a new scaling limit and conformal covariance result for the massive and the directed loop-erased random walk.
This talk is based on joint work with Nathanaël Berestycki (Vienna)