A lower bound for disconnection by random interlacements

Abstract

We consider the vacant set of random interlacements on Z^d, with d bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, 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 arXiv:1304.7477.

arXiv comment28 pages, appeared in the Electronic Journal of Probability

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• On the cost of the bubble set for random interlacements
• Critical surface of the hexagonal polygon model
• Phase transition for level-set percolation of the membrane model in dimensions $d\ge 5$
• Disconnection and level-set percolation for the Gaussian free field
• Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection