Large Deviations for Occupation Time Profiles of Random Interlacements

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 Z, d ≥ 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 R, 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. Departement Mathematik ETH Zürich CH-8092 Zürich Switzerland This research was supported in part by the grant ERC-2009-AdG 245728-RWPERCRI