Conformal loop ensembles: the Markovian characterization and the loop-soup construction

摘要

For random collections of self-avoiding loops in two-dimensional do-mains, we dene a simple and natural conformal restriction property that is conjecturally satised by the scaling limits of interfaces in models from statistical physics. This property is basically the combination of confor-mal invariance and the locality of the interaction in the model. Unlike the Markov property that Schramm used to characterize SLE curves (which involves conditioning on partially generated interfaces up to arbitrary stop-ping times), this property only involves conditioning on entire loops and thus appears at rst glance to be weaker.