Absence of percolation in the Bernoulli Boolean model

Cristian F. Coletti; Sebastian P. Grynberg

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arXiv · 1402.3118

Absence of percolation in the Bernoulli Boolean model

Cristian F. Coletti·Sebastian P. Grynberg

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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.

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Cristian F. Coletti, Sebastian P. Grynberg. 2014-02-13. Absence of percolation in the Bernoulli Boolean model. https://arxiv.org/abs/1402.3118

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