On the crossing estimates for simple conformal loop ensembles

Tianyi Bai, Yijun Wan

We prove the super-exponential decay of probabilities that there exist $n$ crossings of a given quadrilateral in a simple ${\text{CLE}}_{\kappa }(\Omega )$, $\frac{8}{3}<\kappa \le 4$, as $n$ goes to in…