  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.
