On scaling limits and Brownian interlacements

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.

28 pages, typos corrected, appeared in the special issue of the Bulletin of the Brazilian Mathematical Society-IMPA 60 years

References in corpus (2)

• Cover times in the discrete cylinder
• On the easiest way to connect $k$ points in the Random Interlacements process

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• Percolative properties of Brownian interlacements and its vacant set
• Percolation for the Finitary Random interlacements
• Intersection local times for interlacements
• Percolation for two-dimensional excursion clouds and the discrete Gaussian free field
• On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements
• A Ray-Knight theorem for $\nabla \varphi$ interface models and scaling limits
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