Percolation in a multiscale Boolean model

2010/09/20 by Jean-Baptiste Gouéré, Gouéré, Jean-Baptiste
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1009.3719

arxiv created 2011/03/11 · arxiv updated 2011/03/14

Abstract

We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the n^\textrmth copy is ρ^-n. We prove, under optimal integrability assumptions, that no percolation occurs in the multiscale Boolean model for large enough ρ if the rate of the Boolean model is below some critical value.

Related

• Subcritical sharpness for multiscale Boolean percolation
• Percolation in the Boolean model with convex grains in high dimension
• Equivalence of some subcritical properties in continuum percolation
• Subcritical regimes in some models of continuum percolation
• Absence of percolation in the Bernoulli Boolean model