Eveliina Peltola: Multiple SLEs for $\kappa \leq 4$

We consider conformally invariant measures on curves known as multiple Schramm-Loewner evolutions (SLEs), that naturally correspond to interfaces in critical planar lattice models with alternating boundary conditions (i.e. generalized Dobrushin boundary conditions). We give an explicit construction of the multiple SLE measures using the Brownian loop measure (when \(\kappa \leq 4\)). By a Markov chain argument, we show that the multiple SLEs are uniquely characterized by a natural cascade property.
The talk is based on joint works with Hao Wu (Yau Mathematical Sciences Center, Tsinghua University) and Vincent Beffara (Université Grenoble Alpes, Institut Fourier).