Boolean percolation on digraphs and random exchange processes

Abstract

We study, in a general graph-theoretic formulation, a long-range percolation model introduced by Lamperti. For various underlying directed graphs, we discuss connections between this model and random exchange processes. We clarify, for $n\in \mathbb{N}$, under which conditions the lattices ${\mathbb{N}}_0^n$ and ${\mathbb{Z}}^n$ are essentially covered in this model. Moreover, for all $n\ge 2$, we establish that it is impossible to cover the directed $n$-ary tree in our model.

14 pages

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• Subcritical regimes in the Poisson Boolean model of continuum percolation
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Cited by in corpus (1)

• Subcritical Boolean percolation on graphs of bounded degree