A new computation of pairing probabilities in several multiple-curve models

Abstract

We give a new, short computation of pairing probabilities for multiple chordal interfaces in the critical Ising model, the harmonic explorer, and for multiple level lines of the Gaussian free field. The core of the argument are the known convexity property and a new uniqueness property of local multiple SLE$(\kappa)$ measures, valid for all $\kappa > 0$. In particular, the proof is directly is applicable for any underlying random curve model, once it is identified as a local multiple SLE$(\kappa)$ both conditionally and unconditionally on the pairing topology.