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Local percolative properties of the vacant set of random interlacements with small intensity

Alexander Drewitz;  Balázs Ráth;  Artëm Sapozhnikov — 2014

Annales de l'I.H.P. Probabilités et statistiques

Random interlacements at level u is a one parameter family of connected random subsets of ℤ d , d ≥ 3 ( (2010) 2039–2087). Its complement, the vacant set at level u , exhibits a non-trivial percolation phase transition in u ( (2009) 831–858; (2010) 2039–2087), and the infinite connected component, when it exists, is almost surely unique ( (2009) 454–466). In this paper we study local percolative properties of the vacant set of random interlacements...

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