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Journal articles

Equivalence of some subcritical properties in continuum percolation

Abstract : We consider the Boolean model on Rd. We prove some equivalences between subcritical percolation properties. Let us introduce some notations to state one of these equivalences. Let C denote the connected component of the origin in the Boolean model. Let |C| denotes its volume. Let ℓ denote the maximal length of a chain of random balls from the origin. Under optimal integrability conditions on the radii, we prove that E(|C|) is finite if and only if there exists A,B > 0 such that P(ℓ ≥ n) ≤ Ae−Bn for all n ≥ 1.
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Contributor : Marie Théret Connect in order to contact the contributor
Submitted on : Thursday, March 4, 2021 - 9:52:04 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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Jean-Baptiste Gouéré, Marie Théret. Equivalence of some subcritical properties in continuum percolation. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2019, 25 (4B), pp.3714-3733. ⟨10.3150/19-BEJ1108⟩. ⟨hal-03158712⟩



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