Abstract
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*.
Citation
Augusto Teixeira. "On the uniqueness of the infinite cluster of the vacant set of random interlacements." Ann. Appl. Probab. 19 (1) 454 - 466, February 2009. https://doi.org/10.1214/08-AAP547
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