Abstract
Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability