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January 2016 Nonoptimality of constant radii in high dimensional continuum percolation
Jean-Baptiste Gouéré, Régine Marchand
Ann. Probab. 44(1): 307-323 (January 2016). DOI: 10.1214/14-AOP974


Consider a Boolean model $\Sigma$ in $\mathbb{R}^{d}$. 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.


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Jean-Baptiste Gouéré. Régine Marchand. "Nonoptimality of constant radii in high dimensional continuum percolation." Ann. Probab. 44 (1) 307 - 323, January 2016.


Received: 1 March 2013; Revised: 1 September 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1342.60167
MathSciNet: MR3456339
Digital Object Identifier: 10.1214/14-AOP974

Primary: 60K35 , 82B43

Keywords: Boolean model , continuum percolation , percolation

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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