Percolation in the Boolean model with convex grains in high dimension
Probability
2020-12-09 v1
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 K for a further parameter (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.
Cite
@article{arxiv.2012.04370,
title = {Percolation in the Boolean model with convex grains in high dimension},
author = {Jean-Baptiste Gouéré and Florestan Labéy},
journal= {arXiv preprint arXiv:2012.04370},
year = {2020}
}