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A lower bound for disconnection by random interlacements. (English) Zbl 1355.60035
Summary: We consider the vacant set of random interlacements on \(\mathbb{Z}^d\), with \(d\) bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work [Probab. Theory Relat. Fields 161, No. 1–2, 309–350 (2015; Zbl 1314.60078)], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates the problem to some of the large deviations of the occupation-time profile considered in [loc. cit.].

MSC:
60F10 Large deviations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J27 Continuous-time Markov processes on discrete state spaces
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