Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process

Abstract

We consider the Brownian interlacements model in Euclidean space, introduced by A.S. Sznitman in \cite{sznitman2013scaling}. We give estimates for the asymptotics of the visibility in the vacant set. We also consider visibility inside the vacant set of the Brownian excursion process in the unit disc and show that it undergoes a phase transition regarding visibility to infinity as in \cite{benjamini2009visibility}. Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.