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

Abstract

We investigate percolation of the vacant set of random interlacements on ${\mathbb{Z}}^d$, $d\ge 3$, 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 $A\subseteq {\mathbb{R}}^d$ 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 ${\mathbb{Z}}^d$, $d\ge 3$, have been obtained by the authors in arxiv:1808.09947. Our proofs rely crucially on the `solidification estimates' developed in arXiv:1706.07229 by A.-S. Sznitman and the second author.

35 pages, 2 figures, accepted in the Annals of Probability

References in corpus (3)

• On macroscopic holes in some supercritical strongly dependent percolation models
• Solidification of porous interfaces and disconnection
• Disconnection by level sets of the discrete Gaussian free field and entropic repulsion