an:07116306
Zbl 07116306
Elias, Olof; Tykesson, Johan
Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process
EN
ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 2, 1007-1028 (2019).
00435704
2019
j
60K35 82B43
Brownian interlacements; Brownian excursions; visibility
Summary: We consider the Brownian interlacements model in Euclidean space, introduced by \textit{A.-S. Sznitman} [Bull. Braz. Math. Soc. (N.S.) 44, No. 4, 555--592 (2013; Zbl 1303.60022)]. 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 [\textit{I. Benjamini} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 6, 323--342 (2009; Zbl 1276.82012)]. Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.
Reviewer (Berlin)
Zbl 1303.60022; Zbl 1276.82012