摘要
We prove a super-exponential decay of probabilities that there exist n crossings of a given quad for a simple CLE kappa (Omega), 8/3 < kappa <= 4, as n goes to infinity. Besides, being of independent interest, this also provides the missing ingredient in [2] for proving the convergence of probabilities of cylindrical events for the double-dimer loop ensembles to those for the nested CLE4 (Omega).