On the connectivity of the Poisson process on fractals
Gady Kozma, Zvi Lotker, Gideon Stupp
Abstract
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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