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On the C 1-Property of the Percolation Function of Random Interlacements and a Related Variational Problem
We consider random interlacements on \({\mathbb Z}^d\), d ≥ 3. We show that the percolation function that to each u ≥ 0 attaches the probability that the origin does not belong to an infinite cluster of the vacant set at level u, is C1 on an interval \([0,\widehat {u})\), where …