On the connectivity of the Poisson process on fractals

Details On the connectivity of the Poisson process on fractals On the connectivity of the Poisson process on fractals

2006-04-11

arxiv.org/abs/math/0604261v1

Mathematics

Probability

5 pages

Scientific paper

For a measure mu supported on a compact connected subset of a Euclidean space
which satisfies a uniform d-dimensional decay of the volume of balls we show
that the maximal edge in the minimum spanning tree of n indepndent samples from
mu is, with high probability (log n/n)^(1/d).

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