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1 results

Boolean percolation on digraphs and random exchange processes
Part of
- Markov processes
- Equilibrium statistical mechanics
Georg Braun
Journal:

Journal of Applied Probability / Volume 61 / Issue 3 / September 2024

Published online by Cambridge University Press:

25 October 2023, pp. 755-766

Print publication:

September 2024
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We study in a general graph-theoretic formulation a long-range percolation model introduced by Lamperti [27]. For various underlying digraphs, we discuss connections between this model and random exchange processes. We clarify, for all $n \in \mathbb{N}$, under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$, we establish that it is impossible to cover the directed n-ary tree in our model.