Entropic repulsion for the occupation-time field of Random interlacements conditioned on disconnection

We investigate percolation of the vacant set of random interlacements on Z^d, d ≥ 3, in the strongly percolative regime. We consider the event that the interlacement set at level u disconnects the discrete blow-up of a compact set A ⊆ R^d from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the occupation times deviate from a specific function depending on the harmonic potential of A, when disconnection occurs. If certain critical levels coincide, which is plausible but open at the moment, these bounds imply that conditionally on disconnection, the occupation-time profile undergoes an entropic push governed by a specific function depending on A. Similar entropic repulsion phenomena conditioned on disconnection by level-sets of the discrete Gaussian free field on Z^d, d ≥ 3, have been obtained by the authors in (Chiarini and Nitzschner (2018). Our proofs rely crucially on the "solidification estimates" developed in (Nitzschner and Sznitman (2017).