Percolation in the Boolean model with convex grains in high dimension

2020/12/08 by Gouéré, Jean-Baptiste, Labéy, Florestan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.04370

Abstract

We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K ⊂ R d with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or ρK for a further parameter ρ ∈ (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.

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