From conformal invariance of parafermionic observables to conformal invariance of interfaces of planar randomcluster models
From conformal invariance of parafermionic observables to conformal invariance of interfaces of planar randomcluster models

Hugo Duminil  Copin , University of Geneva
Jadwin Hall A06
In this talk we will explain how the determination of the scaling limit of parafermionic observables can be used to deduce the conformal invariance of interfaces in planar randomcluster models with clusterweight 1 ≤ Q ≤ 4 (1\leq Q \leq 4). The strategy was introduced in the context of the looperased random walk by LawlerSchrammWerner, and was implemented for the FK Ising model (a.k.a. the randomcluster model with clusterweight equal to 2) by Chelkak, DuminilCopin, Hongler, Kemppainen and Smirnov, based on a main contribution of Smirnov.