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 Z^d, with d bigger or equal to 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^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.

38 pages, typos corrected, more explanations, appears in Probability Theory and Related Fields

References in corpus (1)

• On scaling limits and Brownian interlacements

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