HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
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.
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03158712
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

Links full text

Identifiers

Relations

Citation

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⟩

Share

Metrics

Record views

39