Nonoptimality of constant radii in high dimensional continuum percolation

• Gouéré, Jean-Baptiste ^[1] ; Marchand, Régine ^[2]
  1. [1] University of Orléans

     University of Orléans

     Arrondissement d’Orléans, Francia

     
  2. [2] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 307-323
• Idioma: inglés
• DOI: 10.1214/14-AOP974
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• Resumen

  • Consider a Boolean model Σ in Rd. The centers are given by a homogeneous Poisson point process with intensity λ and the radii of distinct balls are i.i.d. with common distribution ν. The critical covered volume is the proportion of space covered by Σ when the intensity λ is critical for percolation. Previous numerical simulations and heuristic arguments suggest that the critical covered volume may be minimal when ν is a Dirac measure. In this paper, we prove that it is not the case in sufficiently high dimension.