Absence of percolation in the Bernoulli Boolean model
Probability
2014-02-14 v1
Abstract
We consider the Bernoulli Boolean discrete percolation model on the d-dimensional integer lattice. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the absence of percolation, provided that the intensity of the underlying point process is small enough. We also study a Harris graphical procedure to construct, forward in time, particle systems with interactions of infinite range under the assumption that the corresponding generator admits a Kalikow-type decomposition. We do so by using the subcriticality of the boolean model of discrete percolation.
Cite
@article{arxiv.1402.3118,
title = {Absence of percolation in the Bernoulli Boolean model},
author = {Cristian F. Coletti and Sebastian P. Grynberg},
journal= {arXiv preprint arXiv:1402.3118},
year = {2014}
}