On scaling limits and Brownian interlacements

TL;DR

This paper studies the scaling limits of occupation times for continuous-time interlacements on Z^d, revealing connections to Brownian interlacements and the Gaussian free field, and extends an isomorphism theorem in three dimensions.

Contribution

It introduces the scaling limits of occupation times for interlacements, linking them to Brownian interlacements and the Gaussian free field, and derives a new isomorphism theorem in three dimensions.

Findings

Scaling limit of occupation times leads to Brownian interlacements.

High intensity regime relates to the Gaussian free field.

New isomorphism theorem established for d=3.

Abstract

We consider continuous time interlacements on Z^d, with d bigger or equal to 3, and investigate the scaling limit of their occupation times. In a suitable regime, referred to as the constant intensity regime, this brings Brownian interlacements on R^d into play, whereas in the high intensity regime the Gaussian free field shows up instead. We also investigate the scaling limit of the isomorphism theorem of arXiv:1111.4818. As a by-product, when d=3, we obtain an isomorphism theorem for Brownian interlacements.