Teixeira, Augusto, On the uniqueness of the infinite cluster of the vacant set of random interlacements, Annals of applied probability , 19(1), 2009, pp. 454-466
We consider the model of random interlacements on .d introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in u of the probability that the origin belongs to the infinite component of the vacant set at level u in the supercritical phase u<u*.