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August 2009 Subcritical regimes in some models of continuum percolation
Jean-Baptiste Gouéré
Ann. Appl. Probab. 19(4): 1292-1318 (August 2009). DOI: 10.1214/08-AAP575


We consider some continuum percolation models. We are mainly interested in giving some sufficient conditions for the absence of percolation. We give some general conditions and then focus on two examples. The first one is a multiscale percolation model based on the Boolean model. It was introduced by Meester and Roy and subsequently studied by Menshikov, Popov and Vachkovskaia. The second one is based on the stable marriage of Poisson and Lebesgue introduced by Hoffman, Holroyd and Peres and whose percolation properties have been studied by Freire, Popov and Vachkovskaia.


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Jean-Baptiste Gouéré. "Subcritical regimes in some models of continuum percolation." Ann. Appl. Probab. 19 (4) 1292 - 1318, August 2009.


Published: August 2009
First available in Project Euclid: 27 July 2009

zbMATH: 1172.60335
MathSciNet: MR2538071
Digital Object Identifier: 10.1214/08-AAP575

Primary: 60G55 , 60K35 , 82B43

Keywords: Boolean percolation , continuum percolation , marriage of Poisson and Lebesgue , multiscale percolation

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 4 • August 2009
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