On the connectivity of the Poisson process on fractals

2006/04/11 by Kozma, Gady, Lotker, Zvi, Stupp, Gideon
#28A80 #60D05 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0604261

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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