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The vacant set of two-dimensional critical random interlacement is infinite. (English) Zbl 1409.60140
Summary: 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 [the first author et al., Commun. Math. Phys. 343, No. 1, 129–164 (2016; Zbl 1336.60185)]. 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.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G50 Sums of independent random variables; random walks
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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