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

Abstract : For the model of two-dimensional random interlacements in the critical regime (i.e., α = 1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [8]. 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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https://hal.archives-ouvertes.fr/hal-01336837
Contributor : Francis Comets <>
Submitted on : Friday, June 24, 2016 - 12:00:41 AM
Last modification on : Saturday, March 28, 2020 - 2:17:27 AM
Document(s) archivé(s) le : Sunday, September 25, 2016 - 10:21:00 AM

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  • HAL Id : hal-01336837, version 1
  • ARXIV : 1606.05805

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Francis Comets, Serguei Popov. The vacant set of two-dimensional critical random interlacement is infinite. 2016. ⟨hal-01336837⟩

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