# Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line

*Viktor Bezborodov*

*Statistics & Probability Letters*, 2021, vol. 176, issue C

**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:** Boolean model; Germ-grain model (search for similar items in EconPapers)

**Date:** 2021

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**DOI:** 10.1016/j.spl.2021.109155

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