Skip to Main content Skip to Navigation
Journal articles

Nonoptimality of constant radii in high dimensional continuum percolation

Abstract : Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is the proportion of space covered by $\Sigma$ when the intensity $\lambda$ is critical for percolation. Previous numerical simulations and heuristic arguments suggest that the critical covered volume may be minimal when $\nu$ is a Dirac measure. In this paper, we prove that it is not the case in sufficiently high dimension.
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download
Contributor : Jean-Baptiste Gouéré Connect in order to contact the contributor
Submitted on : Thursday, September 25, 2014 - 6:20:01 PM
Last modification on : Wednesday, November 3, 2021 - 4:49:21 AM
Long-term archiving on: : Friday, December 26, 2014 - 11:21:26 AM


Files produced by the author(s)



Jean-Baptiste Gouéré, Régine Marchand. Nonoptimality of constant radii in high dimensional continuum percolation. Annals of Probability, Institute of Mathematical Statistics, 2016, 44 (1), pp.307-323. ⟨10.1214/14-AOP974⟩. ⟨hal-01068557⟩



Record views


Files downloads