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

Alberto Chiarini (Corresponding author), Maximilian Nitzschner (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We investigate percolation of the vacant set of random interlacements on Zd, 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 ⊆ Rd 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 Zd, 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).

Original languageEnglish
Pages (from-to)1317-1351
Number of pages35
JournalAnnals of Probability
Volume48
Issue number3
DOIs
Publication statusPublished - May 2020

Keywords

  • Entropic repulsion
  • Large deviations
  • Percolation
  • Random interlacements

Fingerprint Dive into the research topics of 'Entropic repulsion for the occupation-time field of Random interlacements conditioned on disconnection'. Together they form a unique fingerprint.

Cite this