Piecewise Temperleyan dimers and hypergeometric SLE

Abstract：

Thedimermodelisoneofthesimplestbutalsomostintriguingmodelsofstatis- tical mechanics. It is typically studied through its height function, which turns the dimer model into a model of random surfaces. The main question is its large scale behaviour. A remarkable conjecture of Kenyon and Okunkov predicts that the large scale behaviour is in great generality described by the Gaussian free field. This conjecture was proved by Kenyon in the case of Temperleyan boundary conditions. We generalized this result to the piecewise Temperleyan and simply connected domains. Our method is based on considering the span- ning tree associated to this model via Temperley s bijection. As a byproduct, we showed that the hypergeometric SLEs (hSLEs) reduces to a more standard SLEs(p) conditional on the hitting point. This talk is based on a joint work with Nathanaël Berestycki.