  For the model of two-dimensional random interlacements in the critical regime
(i.e., $\alpha=1$), we prove that the vacant set is a.s.\ infinite, thus
solving an open problem from arXiv:1502.03470. Also, we prove that the entrance
measure of simple random walk on annular domains has certain regularity
properties; this result is useful when dealing with soft local times for
excursion processes.
