# Non-optimality of constant radii in high dimensional continuum percolation

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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine

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 $u$. 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 $u$ is a Dirac measure. In this paper, we prove that it is not the case in sufficiently high dimension.

Keywords : Poisson point process branching process Continuum percolation phase transition high dimension

Autor: Jean-Baptiste Gouéré - Régine Marchand -

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

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