On Crossing Probabilities in Critical Random-Cluster Models

I will discuss exact solvability results (in a sense) for scaling limits of interface crossings in critical random-cluster models in the plane with various general boundary conditions.

The results are rigorous for the FK-Ising model, Bernoulli percolation, uniform spanning trees, and the spin-Ising model in appropriate setups. The scaling limit formulas describe structures in the corresponding boundary conformal field theory, falling outside of the realm of minimal models.

Based on joint works with Yu Feng, Mingchang Liu, and Hao Wu - all at Tsinghua University, China.