Large deviations for occupation time profiles of random interlacements

TL;DR

This paper establishes large deviation principles for occupation time profiles of random and Brownian interlacements in large boxes, providing insights into rare events like insulation of macroscopic bodies and deriving new identities for occupation measures.

Contribution

It introduces large deviation principles for occupation times of random and Brownian interlacements, and derives a novel Laplace transform identity based on Schrödinger semi-groups.

Findings

Large deviation principle for occupation time profiles in Z^d and R^d.

Asymptotic analysis of high-density events insulating macroscopic bodies.

New identity for the Laplace transform of occupation-time measures.

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.