Comets, Francis et Popov, Serguei, The vacant set of two-dimensional critical random interlacement is infinite, Annals of probability (Online) , 45(6B), 2017, pp. 4752-4785
For the model of two-dimensional random interlacements in the critical regime (i.e., .=1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [Commun. Math. Phys. 343 (2016) 129.164]. 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.