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May 2020 Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection
Alberto Chiarini, Maximilian Nitzschner
Ann. Probab. 48(3): 1317-1351 (May 2020). DOI: 10.1214/19-AOP1393

Abstract

We investigate percolation of the vacant set of random interlacements on $\mathbb{Z}^{d}$, $d\geq 3$, 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 $\mathbb{Z}^{d}$, $d\geq 3$, 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)).

Citation

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Alberto Chiarini. Maximilian Nitzschner. "Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection." Ann. Probab. 48 (3) 1317 - 1351, May 2020. https://doi.org/10.1214/19-AOP1393

Information

Received: 1 February 2019; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226362
MathSciNet: MR4112716
Digital Object Identifier: 10.1214/19-AOP1393

Subjects:
Primary: 60F10, 60G60, 60J27, 60K35, 82B43

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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