Work

Percolation in the Boolean model with convex grains in high dimension

Year: 2023

Type: article

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⊂Rd 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.

Source: Electronic Journal of Probability

DOI: 10.1214/23-ejp997

Authors: Jean-Baptiste Gouéré, Florestan Labéy

Institutions: Université de Tours, Institut Denis Poisson

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Agence Nationale de la Recherche