1304.7477 (Xinyi Li et al.)

Large deviations for occupation time profiles of random interlacements    [PDF]

Xinyi Li, Alain-Sol Sznitman

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 Schr\"odinger semi-groups.

View original: http://arxiv.org/abs/1304.7477