On the connectivity of the Poisson process on fractals

Research paper by Gady Kozma, Zvi Lotker, Gideon Stupp

Indexed on: 11 Apr '06Published on: 11 Apr '06Published in: Mathematics - Probability


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).