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Percolation in the Boolean model with convex grains in high dimension

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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https://hal.archives-ouvertes.fr/hal-03044355
Contributor : Florestan Labey <>
Submitted on : Monday, December 7, 2020 - 5:26:34 PM
Last modification on : Monday, December 14, 2020 - 5:26:08 PM

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  • HAL Id : hal-03044355, version 1
  • ARXIV : 2012.04370

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Jean-Baptiste Gouéré, Florestan Labéy. Percolation in the Boolean model with convex grains in high dimension. 2020. ⟨hal-03044355⟩

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