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Existence of an unbounded vacant set for subcritical continuum percolation
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32018 (English)In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 23, article id 63Article in journal (Refereed) Published
Abstract [en]

We consider the Poisson Boolean percolation model in R-2, where the radius of each ball is independently chosen according to some probability measure with finite second moment. For this model, we show that the two thresholds, for the existence of an unbounded occupied and an unbounded vacant component, coincide. This complements a recent study of the sharpness of the phase transition in Poisson Boolean percolation by the same authors. As a corollary it follows that for Poisson Boolean percolation in R-d, for any d >= 2, finite moment of order d is both necessary and sufficient for the existence of a nontrivial phase transition for the vacant set.

Place, publisher, year, edition, pages
2018. Vol. 23, article id 63
Keywords [en]
percolation, phase transition, dependent environments
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-161234DOI: 10.1214/18-ECP152ISI: 000444727200008OAI: oai:DiVA.org:su-161234DiVA, id: diva2:1256800
Available from: 2018-10-18 Created: 2018-10-18 Last updated: 2018-10-18Bibliographically approved

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