Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line
Probability
2021-08-30 v2
Abstract
It is well known that there are two regimes in a standard one-dimensional Boolean percolation model: either the entire space is covered a.s., or the covered volume fraction is strictly less than one. The aim of this work is to demonstrate that there is a third possibility in a Boolean model with totally asymmetric grains on a half-line: a.s. there is no unbounded component, but the covered volume fraction is one. An explicit condition is given characterizing the existence of an unbounded occupied component.
Keywords
Cite
@article{arxiv.2009.00742,
title = {Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line},
author = {Viktor Bezborodov},
journal= {arXiv preprint arXiv:2009.00742},
year = {2021}
}