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arXiv · 1606.05805

The vacant set of two-dimensional critical random interlacement is infinite

Francis Comets·Serguei Popov
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Abstract

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.

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Francis Comets, Serguei Popov. 2016-06-18. The vacant set of two-dimensional critical random interlacement is infinite. https://doi.org/10.1214/17-aop1177

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