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We consider the model of random interlacements on ℤd 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*.
Augusto Teixeira (2009) studied this question.