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 Schr\"odinger semi-groups.
Keywords
Cite
@article{arxiv.1304.7477,
title = {Large deviations for occupation time profiles of random interlacements},
author = {Xinyi Li and Alain-Sol Sznitman},
journal= {arXiv preprint arXiv:1304.7477},
year = {2015}
}
Comments
38 pages, typos corrected, more explanations, appears in Probability Theory and Related Fields