1209.4531 (Alain-Sol Sznitman)

On scaling limits and Brownian interlacements    [PDF]

Alain-Sol Sznitman

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.

View original: http://arxiv.org/abs/1209.4531