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Large deviations for occupation time profiles of random interlacements

Abstract

We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of \({\mathbb { Z}}^d\), \(d \ge 3\). As an application, we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box. As a step in this program, we obtain a similar large deviation principle for the occupation-time measure of Brownian interlacements at a fixed level in a large box of \({\mathbb { R}}^d\), and we derive a new identity for the Laplace transform of the occupation-time measure, which is based on the analysis of certain Schrödinger semi-groups.

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Correspondence to Alain-Sol Sznitman.

Additional information

This research was supported in part by the grant ERC-2009-AdG 245728-RWPERCRI.

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Li, X., Sznitman, AS. Large deviations for occupation time profiles of random interlacements. Probab. Theory Relat. Fields 161, 309–350 (2015). https://doi.org/10.1007/s00440-014-0550-3

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Mathematics Subject Classification

  • 60F10
  • 60G60
  • 60J45
  • 60K35