A near neighbour continuum percolation model

Details A near neighbour continuum percolation model A near neighbour continuum percolation model

2006-11-10

arxiv.org/abs/math/0611315v1

Mathematics

Probability

18 pages

Scientific paper

We introduce a continuum percolation model defined on the points of a
d-dimensional homogeneous Poisson process. Each Poisson point is connected to
all points within its connection range, which depends on the distances to the
other Poisson points. We show that the new model exhibits a phase transition,
and obtain results about the critical values in low and high dimensions.

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