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Large deviations for occupation time profiles of random interlacements. (English) Zbl 1314.60078
Authors’ 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 $${\mathbb Z}^d$$, $$d \geq 3.$$ 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 semigroups.

##### MSC:
 60F10 Large deviations 60G60 Random fields 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J45 Probabilistic potential theory
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