Two-dimensional random interlacements: 0-1 law and the vacant set at criticality

Abstract

We correct and streamline the proof of the fact that, at the critical point $\alpha =1$, the vacant set of the two-dimensional random interlacements is infinite (Comets, Popov, 2017). Also, we prove a zero-one law for a natural class of tail events related to the random interlacements.

revised version, 14 pages, 2 pictures; corrects a flaw contained in the final part of the proof in arXiv:1606.05805