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November 2017 The vacant set of two-dimensional critical random interlacement is infinite
Francis Comets, Serguei Popov
Ann. Probab. 45(6B): 4752-4785 (November 2017). DOI: 10.1214/17-AOP1177

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 [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.

Citation

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Francis Comets. Serguei Popov. "The vacant set of two-dimensional critical random interlacement is infinite." Ann. Probab. 45 (6B) 4752 - 4785, November 2017. https://doi.org/10.1214/17-AOP1177

Information

Received: 1 July 2016; Revised: 1 November 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838132
MathSciNet: MR3737923
Digital Object Identifier: 10.1214/17-AOP1177

Subjects:
Primary: 60K35
Secondary: 60G50, 82C41

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 6B • November 2017
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