English

Large deviations for occupation time profiles of random interlacements

Probability 2015-02-09 v2 Mathematical Physics math.MP

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

R2 v1 2026-06-22T00:07:40.775Z