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We investigate percolation of the vacant set of random interlacements on$\mathbb{Z}^d$, $d\geq 3$, in the strongly percolative regime. We consider theevent that the interlacement set at level $u$ disconnects the discrete blow-upof a compact set $A\subseteq \mathbb{R}^d$ from the boundary of an enclosingbox. We derive asymptotic large deviation upper bounds on the probability thatthe local averages of the occupation times deviate from a specific functiondepending on the harmonic potential of $A$, when disconnection occurs. Ifcertain critical levels coincide, which is plausible but open at the moment,these bounds imply that conditionally on disconnection, the occupation-timeprofile undergoes an entropic push governed by a specific function depending on$A$. Similar entropic repulsion phenomena conditioned on disconnection bylevel-sets of the discrete Gaussian free field on $\mathbb{Z}^d$, $d \geq 3$,have been obtained by the authors in arxiv:1808.09947. Our proofs relycrucially on the `solidification estimates' developed in arXiv:1706.07229 byA.-S. Sznitman and the second author.

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